# Spacetime and orbits of bumpy black holes

## Abstract

Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced ''bumpy black holes'': objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes--objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find thatmore »

- Authors:

- Department of Physics and MIT Kavli Institute, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 21409091

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.81.024030; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASTROPHYSICS; BLACK HOLES; GENERAL RELATIVITY THEORY; HAMILTON-JACOBI EQUATIONS; MATHEMATICAL SOLUTIONS; MULTIPOLES; PARTICLE TRACKS; POTENTIALS; SPACE-TIME; UNIVERSE; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICS; RELATIVITY THEORY

### Citation Formats

```
Vigeland, Sarah J., and Hughes, Scott A..
```*Spacetime and orbits of bumpy black holes*. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVD.81.024030.

```
Vigeland, Sarah J., & Hughes, Scott A..
```*Spacetime and orbits of bumpy black holes*. United States. doi:10.1103/PHYSREVD.81.024030.

```
Vigeland, Sarah J., and Hughes, Scott A.. Fri .
"Spacetime and orbits of bumpy black holes". United States. doi:10.1103/PHYSREVD.81.024030.
```

```
@article{osti_21409091,
```

title = {Spacetime and orbits of bumpy black holes},

author = {Vigeland, Sarah J. and Hughes, Scott A.},

abstractNote = {Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced ''bumpy black holes'': objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes--objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find that in the weak field, orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is many times greater than would be predicted from a Newtonian analysis, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime's multipoles deviate from the black hole expectation.},

doi = {10.1103/PHYSREVD.81.024030},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 2,

volume = 81,

place = {United States},

year = {2010},

month = {1}

}