arXiv subjects
Publications and source records attributed to Hristu Culetu.
A nonstatic Schwarzschild black hole interior solution in Painleve-Gullstrand coordinates is proposed in this paper, by means of a coordinate transformation that changes the spatial coordinate but the timelike one is preserved. The timelike and null geodesic equations are obtained exactly, taking advantage that the spatial z-coordinate is cyclic.
A null fluid with radial pressure is proposed as the source generating Vaidya spacetime. The fluid is anisotropic with no transversal pressures and $p = ρ/3$ as its equation of state, where $p$ is the isotropic pressure and $ρ$ is the energy density. The radial energy flux is inward directed when $\dot{m} > 0$ and the total energy flow crossing a surface of constant $r$ resembles the Brown-York quasilocal energy. A modified Vaidya metric removes the singularity at the origin and the corresponding QLE is investigated in terms of both $r$ and the mass $m(v)$ of the object.
A version of the Schwarzschild metric to be valid in microphysics is proposed. The source fluid is anisotropic with $p_{r} = -ρ$ and fluctuating tangential pressures. At large distances with respect to the Compton wavelength associated to the source particle, they do not depend on the mass $m$ of the source and everywhere depend on $\hbar$ and the velocity of light $c$ but not on the Newton constant $G$. The particle may be a black hole for $m \geq m_{P}$ only and when $m = m_{P}$ it becomes an extremal black hole. The Komar energy $W$ of the gravitational fluid is $mc^{2}$ for $\hbar = 0$ and at large distances and vanishes at $r_{0} = 2\hbar/emc$. The WEC is violated when $r < r_{0}/2$ due to the negative tangential pressures. The horizon entropy for the extremal black hole is finite though $W$ and the temperature $T$ are vanishing there.
The behaviour of a static thin shell embedded in dS space is investigated. To satisfy the junction conditions at the boundary, one rescales the time variable. The surface energy $σ$ on the shell is positive but its surface tension $τ$ is negative when $r << a$, where $a$ is the horizon radius. The repulsive character of the radial acceleration of a static inner observer is fortified by the process of sinking in the Sitter universe. An upper limit for $σ$ has to be imposed for the shell mass to remain positive.
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $ρ$ and all pressures are finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, the $z$-axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
We study the possibility of shielding a regular extremal black hole by means of a matter thin-shell. While the surface energy density $σ$ on the static shell is negative, the tangential pressures $p$ are positive, both of them being finite when the shell approaches the black hole horizon. The Darmois-Israel junction conditions are used to find $σ$ and $p$ in terms of the radius $a$ of the shell. The surface gravitational energy $E_{S}$ is computed, keeping track of the pressure contribution. The stability conditions are briefly investigated.
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $ξ^{v}$ and $ξ^{u}$ of the separation vector behave as in flat space but the transversal components $ξ^{x}$ and $ξ^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
Few comments upon Ali and Khalil's paper are pointed out. Their modified Schwarzschild metric seems not to be new as it has the same structure as Eq. (2.6) from Ref.4. Their black hole temperature $T$ and heat capacity $C$ correspond exactly to the Reissner-Nordtstrom values, with $\hbar η$ instead of $Q^{2}$. The expression for the black hole entropy turns out to be erronous and does not fit with the other authors' calculations. Moreover, a lot of equations have wrong physical units (terms in the same equation have different units).
We assumed a stress tensor is necessary on the event horizon of a Schwarzschild black hole or on the Rindler horizon for the Israel matching conditions to be satisfied. We found the surface energy density $ρ_{s}$ is vanishing but the surface pressure $p_{s}$ equals $1/16πl$ in both cases, where $l$ is the proper distance from the horizon. The junction relations are applied both for $r =$ const. and $T =$ const. surfaces, with the same results for the surface parameters $ρ_{s}$ and $p_{s}$. We emphasize the nonstatic feature of the spacetimes beyond the corresponding horizons.
A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $ρ= -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. The timelike and null geodesics of the spacetime are examined. A regularized form of the metric is proposed, rendering it finite at the origin. The energy density of the fluid becomes finite and negative for any $r$ and all the pressures are positive throughout the spacetime. The Tolman-Komar energy $W(r)$ is computed and proves to be smaller than that one calculated with the Dadhich metric.
By assuming that the Kehagias-Sfetsos black hole is an exact solution of the standard Einstein equations, we investigate the properties of its source that generates the curvature. The anisotropic fluid has $p_{r} = - ρ$ as equation of state and fulfills the WEC and NEC. The gravitational field is repulsive inside the horizon and attractive outside, becoming of Schwarzschild type at large distances. The Misner-Sharp energy equals the black hole mass asymptotically.
A modified version of the Reissner-Nordstrom metric is proposed on the grounds of the nonlinear electrodynamics model. The source of curvature is an anisotropic fluid with $p_{r} = -ρ$ which resembles the Maxwell stress tensor at $r >> q^{2}/2m$, where $q$ and $m$ are the mass and charge of the particle, respectively. We found the black hole horizon entropy obeys the relation $S = |W|/2T = A_{H}/4$, with $W$ the Komar energy and $A_{H}$ the horizon area. The electric field around the source depends not only on its charge but also on its mass. The corresponding electrostatic potential $Φ(r)$ is finite everywhere, vanishes at the origin and at $r = q^{2}/6m$ and is nonzero asymptotically, with $Φ_{\infty} = 3m/2q$.
The properties of a particular Misner - Thorne wormhole are investigated. The "exotic stress-energy" needed to maintain the wormhole open corresponds to a massless scalar field whose Lagrangean density contains a negative kinetic term. While the Komar energy of the spacetime is vanishing due to the negative energy density and radial pressure, the ADM energy is (minus) the Planck energy. The timelike geodesics are hyperbolae and any static observer is inertial. The null radial trajectories are also hyperbolae and Lorentz invariant as Coleman- de Luccia expanding bubble or Ipser-Sikivie domain wall. Using a different equation of state for the fluid on the dynamic wormhole throat of Redmount and Suen, we reached an equation of motion for the throat (a hyperbola) that leads to a negative surface energy density and the throat expands with the same acceleration $2π|σ|$ as the Ipser-Sikivie domain wall.
A correlation between accelerated motion and a noncompact 5th dimension is proposed. The curvature invariants and the stress energy tensor in the bulk depend only on the 5th dimension $w$ and vanish asymptotically while the proper acceleration of a static observer is proportional to $1/w$. The brane (located at $w = w_{0}$) metric is conformally flat (of AdS type) with $Λ= -3/w_{0}^{2}$ and the invariant acceleration $a = \sqrt{a^{b}a_{b}} = 1/w_{0}$. Therefore, we assume that a hyperbolic observer with the rest-system acceleration $a$ is embedded in the 5th dimension at $w_{0} = 1/a$.
The kinematical quantities derived from the velocity field of a nongeodesic congruence are studied. We found the shear tensor components are finite in time but diverge at the event horizon of the spacetime located at $ρ= 0$. The surface gravity on the horizon is just the proper acceleration of the uniformly expanding distribution of observers, in spherical Rindler coordinates. The Raychaudhuri equation is fulfilled for the congruence of particles worldlines.
We propose a no horizon black hole whose collapsing matter condenses close to the event horizon and before its formation. Compared to Vaz's model [arXiv: 1407.3823], our interior geometry depends only on one parameter $r_{0}$ - the radius of the region where quantum fluctuations are significant. While the equation of state of the inner fluid is $p_{r} = -ρ$ and the traverse pressures are vanishing, the surface stress tensor corresponds to an anisotropic fluid with negative surface tension. Using the junction conditions on the boundary of the collapsing star, we found that $r_{0}$ is half its Schwarzschild radius and not $2M$, as previously obtained by Vaz for a dust ball.
The Shiromizu et al. \cite{SMS} covariant decomposition formalism is used to find out the brane properties rooted from the 5-dimensional Witten bubble spacetime. The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = ρ/3$ as equation of state. The tidal acceleration is towards the brane and that is in accordance with the negative energy density on the brane. The anisotropic fluid has vanishing "bulk" viscosity but the shear viscosity coefficient is $r$- and $t$- dependent. The brane is endowed with an apparent horizon which is exactly the radial null geodesic.
Balasubramanian, Czech, Chowdhury and de Boer \cite{BCCdB} studied a "spherical Rindler space" and found that accelerating observers are causally disconnected from a spherical region located at the origin of Minkowski space. We show that there is no any horizon of size $R_{0}$ (which is related to the chosen initial conditions) and the event horizon at $r = 0$ is obtained only from the two-dimensional ($r, t$) static restriction. Their near-horizon geometry cancels the time dependence of the original metric and therefore the approximation used is doubtful.