35 research outputs found
Velocity and velocity bounds in static spherically symmetric metrics
We find simple expressions for velocity of massless particles in dependence
of the distance in Schwarzschild coordinates. For massive particles these
expressions put an upper bound for the velocity. Our results apply to static
spherically symmetric metrics. We use these results to calculate the velocity
for different cases: Schwarzschild, Schwarzschild-de Sitter and
Reissner-Nordstr\"om with and without the cosmological constant. We emphasize
the differences between the behavior of the velocity in the different metrics
and find that in cases with naked singularity there exists always a region
where the massless particle moves with a velocity bigger than the velocity of
light in vacuum. In the case of Reissner-Nordstr\"om-de Sitter we completely
characterize the radial velocity and the metric in an algebraic way. We
contrast the case of classical naked singularities with naked singularities
emerging from metric inspired by noncommutative geometry where the radial
velocity never exceeds one. Furthermore, we solve the Einstein equations for a
constant and polytropic density profile and calculate the radial velocity of a
photon moving in spaces with interior metric. The polytropic case of radial
velocity displays an unexpected variation bounded by a local minimum and
maximum.Comment: 20 pages, 5 figure
Velocity and velocity bounds in static spherically symmetric metrics
We find simple expressions for velocity of massless particles in dependence
of the distance in Schwarzschild coordinates. For massive particles these
expressions put an upper bound for the velocity. Our results apply to static
spherically symmetric metrics. We use these results to calculate the velocity
for different cases: Schwarzschild, Schwarzschild-de Sitter and
Reissner-Nordstr\"om with and without the cosmological constant. We emphasize
the differences between the behavior of the velocity in the different metrics
and find that in cases with naked singularity there exists always a region
where the massless particle moves with a velocity bigger than the velocity of
light in vacuum. In the case of Reissner-Nordstr\"om-de Sitter we completely
characterize the radial velocity and the metric in an algebraic way. We
contrast the case of classical naked singularities with naked singularities
emerging from metric inspired by noncommutative geometry where the radial
velocity never exceeds one. Furthermore, we solve the Einstein equations for a
constant and polytropic density profile and calculate the radial velocity of a
photon moving in spaces with interior metric. The polytropic case of radial
velocity displays an unexpected variation bounded by a local minimum and
maximum.Comment: 20 pages, 5 figure
Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry
We derive a transformation of the noncommutative geometry inspired
Schwarzschild solution into new coordinates such that the apparent unphysical
singularities of the metric are removed. Moreover, we give the maximal
singularity-free atlas for the manifold with the metric under consideration.
This atlas reveals many new features e.g. it turns out to describe an infinite
lattice of asymptotically flat universes connected by black hole tunnels.Comment: 17 pages LaTex, 2 figure
Time Evolution of Temperature and Entropy of Various Collapsing Domain Walls
We investigate the time evolution of the temperature and entropy of
gravitationally collapsing domain walls as seen by an asymptotic observer. In
particular, we seek to understand how topology and the addition of a
cosmological constant affect the gravitational collapse. Previous work has
shown that the entropy of a spherically symmetric collapsing domain approaches
a constant. In this paper, we reproduce these results, using both a fully
quantum and a semi-classical approach, then we repeat the process for a de
Sitter Schwarzschild domain wall (spherical with cosmological constant) and a
(3+1) BTZ domain wall (cylindrical). We do this by coupling a scalar field to
the background of the domain wall and analyzing the spectrum of radiation as a
function of time. We find that the spectrum is quasi-thermal, with the degree
of thermality increasing as the domain wall approaches the horizon. The thermal
distribution allows for the determination of the temperature as a function of
time, and we find that the late time temperature is very close to the Hawking
temperature and that it also exhibits the proper scaling with the mass. From
the temperature we find the entropy. Since the collapsing domain wall is what
forms a black hole, we can compare the results to those of the standard
entropy-area relation. We find that the entropy does in fact approach a
constant that is close to the Hawking entropy. However, both the de Sitter
Schwarzschild domain wall and the (3+1) BTZ domain wall show periods of
decreasing entropy, which suggests that spontaneous collapse may be prevented.Comment: This paper is a merging of two previously submitted papers: Time
Evolution of Temperature and Entropy of a Gravitationally Collapsing Cylinder
[arXiv:1106.2278]; Time Evolution of Temperature and Entropy of a
Gravitationally Collapsing de Sitter Schwarzschild Domain Wal
A non commutative model for a mini black hole
We analyze the static and spherically symmetric perfect fluid solutions of
Einstein field equations inspired by the non commutative geometry. In the
framework of the non commutative geometry this solution is interpreted as a
mini black hole which has the Schwarzschild geometry outside the event horizon,
but whose standard central singularity is replaced by a self-gravitating
droplet. The energy-momentum tensor of the droplet is of the anisotropic fluid
obeying a nonlocal equation of state. The radius of the droplet is finite and
the pressure, which gives rise to the hydrostatic equilibrium, is positive
definite in the interior.Comment: 10 pages, 2 figures, bibliography enlarged, reference in the
conclusion fixed, some typos correcte
The Minimum and Maximum Temperature of Black Body Radiation
We show, in different ways, that in the ubiquitous phenomenon of black body
radiation there exists a minimum and maximum temperature. These limiting values
are so small and large respectively, that they are of no practical use, except
in an extreme situation of black hole evaporation where they lead to maximum
and minimum mass.Comment: 7 pages, 1 figur
Tunneling of massive and charged particles from noncommutative Reissner-Nordstr\"{o}m black hole
Massive charged and uncharged particles tunneling from commutative
Reissner-Nordstrom black hole horizon has been studied with details in
literature. Here, by adopting the coherent state picture of spacetime
noncommutativity, we study tunneling of massive and charged particles from a
noncommutative inspired Reissner-Nordstrom black hole horizon. We show that
Hawking radiation in this case is not purely thermal and there are correlations
between emitted modes. These correlations may provide a solution to the
information loss problem. We also study thermodynamics of noncommutative
horizon in this setup.Comment: 10 pages, 2 figure
The Hawking-Page crossover in noncommutative anti-deSitter space
We study the problem of a Schwarzschild-anti-deSitter black hole in a
noncommutative geometry framework, thought to be an effective description of
quantum-gravitational spacetime. As a first step we derive the noncommutative
geometry inspired Schwarzschild-anti-deSitter solution. After studying the
horizon structure, we find that the curvature singularity is smeared out by the
noncommutative fluctuations. On the thermodynamics side, we show that the black
hole temperature, instead of a divergent behavior at small scales, admits a
maximum value. This fact implies an extension of the Hawking-Page transition
into a van der Waals-like phase diagram, with a critical point at a critical
cosmological constant size in Plank units and a smooth crossover thereafter. We
speculate that, in the gauge-string dictionary, this corresponds to the
confinement "critical point" in number of colors at finite number of flavors, a
highly non-trivial parameter that can be determined through lattice
simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE
Hawking radiation and thermodynamics of dynamical black holes in phantom dominated universe
The thermodynamic properties of dark energy-dominated universe in the
presence of a black hole are investigated in the general case of a varying
equation-of-state-parameter . We show that all the thermodynamics
quantities are regular at the phantom divide crossing, and particularly the
temperature and the entropy of the dark fluid are always positive definite. We
also study the accretion process of a phantom fluid by black holes and the
conditions required for the validity of the generalized second law of
thermodynamics. As a results we obtain a strictly negative chemical potential
and an equation-of-state parameter Comment: 22 pages,3 figure
Hawking emission from quantum gravity black holes
We address the issue of modelling quantum gravity effects in the evaporation
of higher dimensional black holes in order to go beyond the usual
semi-classical approximation. After reviewing the existing six families of
quantum gravity corrected black hole geometries, we focus our work on
non-commutative geometry inspired black holes, which encode model independent
characteristics, are unaffected by the quantum back reaction and have an
analytical form compact enough for numerical simulations. We consider the
higher dimensional, spherically symmetric case and we proceed with a complete
analysis of the brane/bulk emission for scalar fields. The key feature which
makes the evaporation of non-commutative black holes so peculiar is the
possibility of having a maximum temperature. Contrary to what happens with
classical Schwarzschild black holes, the emission is dominated by low frequency
field modes on the brane. This is a distinctive and potentially testable
signature which might disclose further features about the nature of quantum
gravity.Comment: 36 pages, 18 figures, v2: updated reference list, minor corrections,
version matching that published on JHE