Effective field theory of black hole quasinormal modes in scalar-tensor theories

Franciolini, Gabriele; Hui, Lam; Penco, Riccardo; Santoni, Luca; Trincherini, Enrico

doi:10.1007/jhep02(2019)127

Title: Effective field theory of black hole quasinormal modes in scalar-tensor theories

Abstract

The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasi-normal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background from Schwarzschild is small, we use the WKB method to introduce the notion of “light ring expansion”. This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation.

Authors:

Franciolini, Gabriele ^[1]; Hui, Lam ^[2]; Penco, Riccardo ^[3];

^[4]; Trincherini, Enrico ^[5]

Center for Astroparticle Physics (CAP), Geneva (Switzerland)
Columbia Univ., New York, NY (United States)
Carnegie Mellon Univ., Pittsburgh, PA (United States)
Univ. of Utrecht (Netherlands)
Scuola Normale Superiore, Pisa (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Pisa (Italy)

Publication Date:: Wed Feb 20 00:00:00 EST 2019

Research Org.:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Netherlands organization for scientifi c research (NWO); National Aeronautics and Space Administration (NASA)

OSTI Identifier:: 1612000

Grant/Contract Number:: SC0013528; NXX16AB27G; SC0011941

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS; Physics; Black Holes; Effective Field Theories

Citation Formats


                    Franciolini, Gabriele, Hui, Lam, Penco, Riccardo, Santoni, Luca, and Trincherini, Enrico. Effective field theory of black hole quasinormal modes in scalar-tensor theories.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep02(2019)127.

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                    Franciolini, Gabriele, Hui, Lam, Penco, Riccardo, Santoni, Luca, & Trincherini, Enrico. Effective field theory of black hole quasinormal modes in scalar-tensor theories.  United States.  https://doi.org/10.1007/jhep02(2019)127

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                    Franciolini, Gabriele, Hui, Lam, Penco, Riccardo, Santoni, Luca, and Trincherini, Enrico. Wed .  
"Effective field theory of black hole quasinormal modes in scalar-tensor theories".  United States.  https://doi.org/10.1007/jhep02(2019)127.  https://www.osti.gov/servlets/purl/1612000.

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@article{osti_1612000,

  title        = {Effective field theory of black hole quasinormal modes in scalar-tensor theories},

  author       = {Franciolini, Gabriele and Hui, Lam and Penco, Riccardo and Santoni, Luca and Trincherini, Enrico},

  abstractNote = {The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasi-normal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background from Schwarzschild is small, we use the WKB method to introduce the notion of “light ring expansion”. This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation.},

  doi          = {10.1007/jhep02(2019)127},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 2,

  volume       = 2019,

  place        = {United States},

  year         = {Wed Feb 20 00:00:00 EST 2019},

  month        = {Wed Feb 20 00:00:00 EST 2019}

}

Copy to clipboard

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Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system. We show that over short time scales the evolution is governed bymore »« less
https://doi.org/10.1088/1475-7516/2019/12/020

Full Text Available
Self-force calculations with matched expansions and quasinormal mode sums

Journal Article Casals, Marc ; Dolan, Sam ; Ottewill, Adrian C ; ... - Physical Review. D, Particles Fields

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in amore »« less
https://doi.org/10.1103/PHYSREVD.79.124043
Second-order quasinormal mode of the Schwarzschild black hole

Journal Article Nakano, Hiroyuki ; Ioka, Kunihito - Physical Review. D, Particles Fields

We formulate and calculate the second-order quasinormal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational waves (GW) from a distorted BH, the so-called ringdowns, are well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with a high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numericallymore »« less
https://doi.org/10.1103/PHYSREVD.76.084007
Quasinormal ringing of Kerr black holes: The excitation factors

Journal Article Berti, Emanuele ; Cardoso, Vitor ; Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677-1848 - Physical Review. D, Particles Fields

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted as a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna (LISA). If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A universal, initial data-independent measure of themore »« less
https://doi.org/10.1103/PHYSREVD.74.104020

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Title: Effective field theory of black hole quasinormal modes in scalar-tensor theories

Abstract

Citation Formats

Exploring gravitational theories beyond Horndeski text, January 2014

Quasinormal modes: the characteristic `sound' of black holes and neutron stars journal, November 1999

The effective theory of shift-symmetric cosmologies journal, May 2018

New Post-Newtonian Parameter to Test Chern-Simons Gravity journal, December 2007

How to tell the shape of a wormhole by its quasinormal modes journal, September 2018

Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories journal, April 2018

Black holes and scalar fields journal, October 2015

Essential building blocks of dark energy journal, August 2013

Dressing a black hole with non-minimally coupled scalar field hair journal, May 2005

Effective field theory of modified gravity on the spherically symmetric background: Leading order dynamics and the odd-type perturbations journal, December 2014

Black hole perturbation in the most general scalar-tensor theory with second-order field equations: The odd-parity sector journal, April 2012

Exploring gravitational theories beyond Horndeski journal, February 2015

Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling text, January 2017

Extreme gravity tests with gravitational waves from compact binary coalescences: (II) ringdown journal, April 2018

General theories of linear gravitational perturbations to a Schwarzschild black hole journal, February 2018

Stable wormholes in scalar-tensor theories text, January 2018

Stealth Schwarzschild solution in shift symmetry breaking theories journal, October 2018

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations journal, June 2016

Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories text, January 2017

Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics journal, November 1970

Erratum: Is the Gravitational-Wave Ringdown a Probe of the Event Horizon? [Phys. Rev. Lett. 116 , 171101 (2016)] journal, August 2016

Starting the Universe: stable violation of the null energy condition and non-standard cosmologies journal, December 2006

Numerical simulations of single and binary black holes in scalar-tensor theories: Circumventing the no-hair theorem journal, June 2013

Perturbed black holes in Einstein-dilaton-Gauss-Bonnet gravity: Stability, ringdown, and gravitational-wave emission journal, November 2016

Effective description of higher-order scalar-tensor theories journal, May 2017

Partial Accretion in the Propeller Stage of Low-mass X-Ray Binary Aql X–1 journal, October 2017

Nonexistence of Baryon Number for Static Black Holes journal, March 1972

Quasinormal modes as a distinguisher between general relativity and f ( R ) gravity journal, September 2017

Constraining the polarization content of gravitational waves with astrometry journal, July 2018

No-Hair Theorem for the Galileon journal, June 2013

Scalar Deformations of Schwarzschild Holes and Their Stability journal, February 1998

Asymptotically flat black holes with scalar hair: A review journal, July 2015

Gravitational-wave versus binary-pulsar tests of strong-field gravity journal, July 1998

WKB approximation for inflationary cosmological perturbations journal, April 2003

Essential Building Blocks of Dark Energy text, January 2013

Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA journal, March 2006

Black Holes and Scalar Fields text, January 2015

Can environmental effects spoil precision gravitational-wave astrophysics? journal, May 2014

Gravitational Rainbows: LIGO and Dark Energy at its Cutoff journal, November 2018

Black hole perturbation in the most general scalar-tensor theory with second-order field equations. II. The even-parity sector journal, April 2014

Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown text, January 2018

From k -essence to generalized Galileons journal, September 2011

Cosmic black-hole hair growth and quasar OJ287 journal, May 2012

Soft theorems for shift-symmetric cosmologies journal, March 2018

The effective field theory of multifield inflation journal, April 2012

Neutron-star mergers in scalar-tensor theories of gravity journal, April 2013

Novel ‘‘no-scalar-hair’’ theorem for black holes journal, June 1995

Quasinormal modes of black holes in Horndeski gravity journal, May 2018

The effective field theory of inflation journal, March 2008

Second-order scalar-tensor field equations in a four-dimensional space journal, September 1974

Black hole hair in generalized scalar-tensor gravity: An explicit example journal, December 2014

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity journal, June 2010

Classical and Quantum Consistency of the DGP Model journal, June 2004

Asymptotically flat black holes with scalar hair: a review preprint, January 2015

Stability of Schwarzschild-like solutions in f ( R , G ) gravity models journal, May 2011

Speed of gravitational waves and black hole hair journal, April 2018

Black hole hair in generalized scalar-tensor gravity: An explicit example text, January 2014

Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling journal, March 2018

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories journal, March 2018

Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes journal, September 2017

Stability of a Schwarzschild Singularity journal, November 1957

Behind Horndeski: structurally robust higher derivative EFTs journal, August 2018

Theory-Agnostic Constraints on Black-Hole Dipole Radiation with Multiband Gravitational-Wave Astrophysics journal, June 2016

Black hole normal modes - A semianalytic approach journal, April 1985

Inverse spectrum problem for quasi-stationary states journal, February 2018

Primordial Black Hole Evolution in Tensor-Scalar Cosmology journal, October 1999

Quasinormal modes as a distinguisher between general relativity and f(R) gravity: charged black-holes journal, September 2018

Asymptotically flat black holes in Horndeski theory and beyond journal, April 2017

Multimode black hole spectroscopy journal, January 2019

Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering journal, June 1987

Galileon as a local modification of gravity journal, March 2009

Signs of analyticity in single-field inflation journal, January 2016

Weakly broken galileon symmetry journal, September 2015

Effective Potential for Even-Parity Regge-Wheeler Gravitational Perturbation Equations journal, March 1970

An effective formalism for testing extensions to General Relativity with gravitational waves journal, September 2017

The Mathematical Theory of Black Holes book, January 1984

Testing gravity with the two-body problem preprint, January 2020

Exploring gravitational theories beyond Horndeski
text, January 2014

Quasinormal modes: the characteristic `sound' of black holes and neutron stars
journal, November 1999

The effective theory of shift-symmetric cosmologies
journal, May 2018

New Post-Newtonian Parameter to Test Chern-Simons Gravity
journal, December 2007

How to tell the shape of a wormhole by its quasinormal modes
journal, September 2018

Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories
journal, April 2018

Black holes and scalar fields
journal, October 2015

Essential building blocks of dark energy
journal, August 2013

Dressing a black hole with non-minimally coupled scalar field hair
journal, May 2005

Effective field theory of modified gravity on the spherically symmetric background: Leading order dynamics and the odd-type perturbations
journal, December 2014

Black hole perturbation in the most general scalar-tensor theory with second-order field equations: The odd-parity sector
journal, April 2012

Exploring gravitational theories beyond Horndeski
journal, February 2015

Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling
text, January 2017

Extreme gravity tests with gravitational waves from compact binary coalescences: (II) ringdown
journal, April 2018

General theories of linear gravitational perturbations to a Schwarzschild black hole
journal, February 2018

Stable wormholes in scalar-tensor theories
text, January 2018

Stealth Schwarzschild solution in shift symmetry breaking theories
journal, October 2018

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
journal, June 2016

Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories
text, January 2017

Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics
journal, November 1970

Erratum: Is the Gravitational-Wave Ringdown a Probe of the Event Horizon? [Phys. Rev. Lett. 116 , 171101 (2016)]
journal, August 2016

Starting the Universe: stable violation of the null energy condition and non-standard cosmologies
journal, December 2006

Numerical simulations of single and binary black holes in scalar-tensor theories: Circumventing the no-hair theorem
journal, June 2013

Perturbed black holes in Einstein-dilaton-Gauss-Bonnet gravity: Stability, ringdown, and gravitational-wave emission
journal, November 2016

Effective description of higher-order scalar-tensor theories
journal, May 2017

Partial Accretion in the Propeller Stage of Low-mass X-Ray Binary Aql X–1
journal, October 2017

Nonexistence of Baryon Number for Static Black Holes
journal, March 1972

Quasinormal modes as a distinguisher between general relativity and $f (R)$ gravity
journal, September 2017

Constraining the polarization content of gravitational waves with astrometry
journal, July 2018

No-Hair Theorem for the Galileon
journal, June 2013

Scalar Deformations of Schwarzschild Holes and Their Stability
journal, February 1998

Asymptotically flat black holes with scalar hair: A review
journal, July 2015

Gravitational-wave versus binary-pulsar tests of strong-field gravity
journal, July 1998

WKB approximation for inflationary cosmological perturbations
journal, April 2003

Essential Building Blocks of Dark Energy
text, January 2013

Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
journal, March 2006

Black Holes and Scalar Fields
text, January 2015

Can environmental effects spoil precision gravitational-wave astrophysics?
journal, May 2014

Gravitational Rainbows: LIGO and Dark Energy at its Cutoff
journal, November 2018

Black hole perturbation in the most general scalar-tensor theory with second-order field equations. II. The even-parity sector
journal, April 2014

Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
text, January 2018

From $k$ -essence to generalized Galileons
journal, September 2011

Cosmic black-hole hair growth and quasar OJ287
journal, May 2012

Soft theorems for shift-symmetric cosmologies
journal, March 2018

The effective field theory of multifield inflation
journal, April 2012

Neutron-star mergers in scalar-tensor theories of gravity
journal, April 2013

Novel ‘‘no-scalar-hair’’ theorem for black holes
journal, June 1995

Quasinormal modes of black holes in Horndeski gravity
journal, May 2018

The effective field theory of inflation
journal, March 2008

Second-order scalar-tensor field equations in a four-dimensional space
journal, September 1974

Black hole hair in generalized scalar-tensor gravity: An explicit example
journal, December 2014

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity
journal, June 2010

Classical and Quantum Consistency of the DGP Model
journal, June 2004

Asymptotically flat black holes with scalar hair: a review
preprint, January 2015

Stability of Schwarzschild-like solutions in $f (R, G)$ gravity models
journal, May 2011

Speed of gravitational waves and black hole hair
journal, April 2018

Black hole hair in generalized scalar-tensor gravity: An explicit example
text, January 2014

Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling
journal, March 2018

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories
journal, March 2018

Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes
journal, September 2017

Stability of a Schwarzschild Singularity
journal, November 1957

Behind Horndeski: structurally robust higher derivative EFTs
journal, August 2018

Theory-Agnostic Constraints on Black-Hole Dipole Radiation with Multiband Gravitational-Wave Astrophysics
journal, June 2016

Black hole normal modes - A semianalytic approach
journal, April 1985

Inverse spectrum problem for quasi-stationary states
journal, February 2018

Primordial Black Hole Evolution in Tensor-Scalar Cosmology
journal, October 1999

Quasinormal modes as a distinguisher between general relativity and f(R) gravity: charged black-holes
journal, September 2018

Asymptotically flat black holes in Horndeski theory and beyond
journal, April 2017

Multimode black hole spectroscopy
journal, January 2019

Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering
journal, June 1987

Galileon as a local modification of gravity
journal, March 2009

Signs of analyticity in single-field inflation
journal, January 2016

Weakly broken galileon symmetry
journal, September 2015

Effective Potential for Even-Parity Regge-Wheeler Gravitational Perturbation Equations
journal, March 1970

An effective formalism for testing extensions to General Relativity with gravitational waves
journal, September 2017

The Mathematical Theory of Black Holes
book, January 1984

Testing gravity with the two-body problem
preprint, January 2020

Stealth black holes in shift symmetric kinetic gravity braiding
journal, January 2020

Perturbations of a rotating black hole in DHOST theories
text, January 2019

Effective field theory of hairy black holes and their flat and de Sitter limits
journal, September 2019