Bounds on the energy densities of ground states on static spacetimes of compact objects

Journal Article · Thu Jun 15 04:00:00 EDT 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.73.124009· OSTI ID:20774892

Marecki, Piotr ^[1]

---

1. Wyzsza Szkola Informatyki i Zarzadzania, 43-300 Bielsko-Biala (Poland)

This paper deals with energy densities of scalar, massless quantum fields propagating on given, static, spherically symmetric, horizon-free spacetimes, such as these of spherical stars. The outer part of the spacetimes is assumed to be described by Schwarzschild metric, while the inner, matter containing part, which begins at the distance l from the horizon of the Schwarzschild spacetime (measured along the spacelike radial geodesic on the surface of constant time on the Schwarzschild spacetime) is left unspecified. We shall put bounds on the ground-state expectation values of locally constructed (that is: by point-splitting and subtraction of the Hadamard singular part) energy-density operators {rho}(t,x-vector), localized in the outer region. These bounds, which are derived from the so-called quantum energy inequalities, limit in absolute the difference between the energy density of ground states and the energy density of the Boulware state (the ground state for Schwarzschild spacetime). The sharpness of the bound from below depends critically on the distance l, but not on the details of internal geometry of the objects. In the limit of small l, we prove that the energy densities of ground states are greater or equal to the Boulware level.

• OSTI ID: 20774892
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COSMOLOGY
DIFFERENTIAL GEOMETRY
DISTANCE
ENERGY DENSITY
GROUND STATES
QUANTUM FIELD THEORY
SCALAR FIELDS
SCHWARZSCHILD METRIC
SPACE-TIME
SPHERICAL CONFIGURATION
VECTORS