Geodesic Deviation in the AdS Black String Spacetime

The equation of motion of test particles in the geometry of a black string embedded in a 5-dimensional AdS spacetime is studied.Comment: 7 page

On the gravitational energy of the Hawking wormhole

The surface energy for a conformally flat spacetime which represents the Hawking wormhole in spherical (static) Rindler coordinates is computed using the Hawking - Hunter formalism for non asymptotically - flat spacetimes. The physical gravitational Hamiltonian is proportional to the Rindler acceleration g of the hyperbolic observer and is finite on the event horizon ksi = b (b-the Planck length, ksi - the Minkowski interval). The corresponding temperature of the system of particles associated to the massless scalar field Psi, coupled conformally to Einstein's equations, is given by the Davies - Unruh temperature up to a constant factor of order unity.Comment: 9 pages, chapter 4 removed, to appear in Int. Jour. Mod. Phys.

Does rotation generate a massive string ?

The properties of a stationary massive string endowed with intrinsic angular momentum are investigated. The spacetime is generated by an "improper" time translation combined with uniform rotation. The mass per unit length of the string is proportional to the angular velocity $\omega$. The spacetime is Minkowskian geometrically but the topology is nontrivial thanks to the event horizon located on the surface $r = 0$ (similar with Rindler's spacetime) and to the deficit angle generated by rotation. The Sagnac time delay is calculated. It proves to be nonvanishing even when $\omega = 0$ due to the intrinsic spin of the string.Comment: 4 pages, minor changes, talk given at the XXIXth Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain, Sept. 4 - 8, 2006, appeared in Jour. Phys. : Conf. Ser. 66 (2007) 01205

Boundary sources in the Doran - Lobo - Crawford spacetime

We take a null hypersurface (the causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the place where the Brown-York quasilocal energy is located. The components of the outer and inner stress tensors are computed and shown to depend on time and on the impact parameter $b$ of the test particle trajectory. The surface energy density $\sigma$ on the boundary is given by the same expression as that obtained previously for the energy stored on a Rindler horizon.Comment: 4 pages, title changed, no figures, minor text change

Thermodynamic Properties of Spherically-Symmetric, Uniformly-Accelerated Reference Frames

We aim to study the thermodynamic properties of the spherically symmetric reference frames with uniform acceleration, including the spherically symmetric generalization of Rindler reference frame and the new kind of uniformly accelerated reference frame. We find that, unlike the general studies about the horizon thermodynamics, one cannot obtain the laws of thermodynamics for their horizons in the usual approaches, despite that one can formally define an area entropy (Bekenstein-Hawking entropy). In fact, the common horizon for a set of uniformly accelerated observers is not always exist, even though the Hawking-Unruh temperature is still well-defined. This result indicates that the Hawking-Unruh temperature is only a kinematic effect, to gain the laws of thermodynamics for the horizon, one needs the help of dynamics. Our result is in accordance with those from the various studies about the acoustic black holes.Comment: 8 page

On the time dependent Schwarzschild - de Sitter spacetime

An imperfect cosmic fluid with energy flux is analyzed. Even though its energy density $\rho$ is positive, the pressure $p = -\rho$ due to the fact that the metric is asymptotically de Sitter. The kinematical quantities for a nongeodesic congruence are computed. The scalar expansion is time independent but divergent at the singularity $r = 2m$. Far from the central mass $m$ and for a cosmic time $\bar{t} << H^{-1}$, the heat flux $q$ does not depend on Newton's constant $G$.Comment: 8 pages, no figures, Sections 3 and 5 enlarged, one reference adde

A Note on Temperature and Energy of 4-dimensional Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be written as $F=\frac{GmM_0}{r^2}$, which could be tested by experiments.Comment: V4: 13 pages, 4 figures, title changed, discussions for experiments added, accepted by CQ

Unwrapping Closed Timelike Curves

Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of a spacetime, one can attempt to change its topology, without changing its geometry, in such a way that the former CTCs are no longer closed in the new spacetime. This procedure is informally known as unwrapping. However, changes in global identifications tend to lead to local effects, and unwrapping is no exception, as it introduces a special kind of singularity, called quasi-regular. This "unwrapping" singularity is similar to the string singularities. We give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Godel spacetime still contains CTCs through every point. A "multiple unwrapping" procedure is devised to remove the remaining circular CTCs. We conclude that, based on the two spacetimes we investigated, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications, but are indeed a necessary consequence of General Relativity, provided only that we demand these solutions do not possess naked quasi-regular singularities.Comment: 29 pages, 9 figure

Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis

We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the flow defined by a state over an observable algebra, and (ii) when this flow is proportional to a geometric flow in spacetime, temperature is the ratio between flow parameter and proper time. An eternal accelerated Unruh observer has access to the local algebra associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a field theory over this algebra is proportional to a flow in spacetime and the associated temperature is the Unruh temperature. An observer with a finite lifetime has access to the local observable algebra associated to a finite spacetime region called a "diamond". The flow defined by the Minkowski vacuum of a (four dimensional, conformally invariant) quantum field theory over this algebra is also proportional to a flow in spacetime. The associated temperature generalizes the Unruh temperature to finite lifetime observers. Furthermore, this temperature does not vanish even in the limit in which the acceleration is zero. The temperature associated to an inertial observer with lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b T).This temperature is related to the fact that a finite lifetime observer does not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte

Quantization of the interior Schwarzschild black hole

We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.Comment: 12 pages, 1 figure, revised versio