We analyze the scalar radiation emitted by a source in a circular geodesic orbit around a spherically symmetric black hole. The black hole spacetime considered is quite general, in the sense that it encompasses the solutions of Schwarzschild and Reissner-Nordström, and also the Bardeen solution of a regular black hole. We use the framework of quantum field theory in curved spaces to compute the one-particle emission amplitude of scalar particles and related quantities.
We address the question of radiation emitted from a collapsing star. We consider the simple model of a spherical star consisting of pressure-free dust and we derive the emission spectrum via a systematic asymptotic expansion of the complete Bogolubov amplitude. We present a review of standard features of the problem and we point out certain inconsistencies in previous derivations.
Using tunnelling approach, Hawking radiation is derived for a general class of non-static spherically symmetric space time. The standard tunnelling rate formula is obtained using the unified first law of thermodynamics on the trapping horizon and Hawking temperature is measured by an Kodama observer inside the horizon.
We recalculate the spectrum of radiation emitted from a collapsing star. We consider the simple model of a spherical star consisting of pressure-free dust and we derive the thermal spectrum via a systematic asymptotic expansion of the complete Bogolubov amplitude. Inconsistencies in previous derivations are pointed out.
Sijie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expected number of particles in any wave packet belonging to $\mathcal{H}_{out}$ spontaneously produced from the state $|0>_{in}$, which confirms the traditional belief that extremal black holes do not radiate particles. Making some modifications, we demonstrate that the analysis can go through for a charged scalar field.
We investigate the radiation emitted from a scalar source in circular orbit around a Reissner-Nordstrom black hole. Particle and energy emission rates are analytically calculated in the low- and high-frequency regimes and shown to be in full agreement with a numerical calculation. Our investigation is connected with the recent discussion on the validity of the cosmic censorship conjecture in the quantum realm.
We analyze the gravitational radiation emitted from a particle in circular motion around a Schwarzschild black hole using the framework of quantum field theory in curved spacetime at tree level. The gravitational perturbations are written in a gauge-invariant formalism for spherically symmetric spacetimes. We discuss the results, comparing them to the radiation emitted by a particle when it is assumed to be orbiting a massive object due to a Newtonian force in flat spacetime.
We present a solution of Einstein equations with quintessential matter surrounding a $d$-dimensional black hole, whose asymptotic structures are determined by the state of the quintessential matter. We examine the thermodynamics of this black hole and find that the mass of the black hole depends on the equation of state of the quintessence, while the first law is universal. Investigating the Hawking radiation in this black hole background, we observe that the Hawking radiation dominates on the brane in the low-energy regime. For different asymptotic structures caused by the equation of state o…
We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness…
Introducing $f(\mathcal{R})$ term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved f…
In this paper, we investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole's mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes …
We analyze the scalar radiation emitted by a source in geodesic circular orbits around a Schwarzschild-de Sitter black hole. We obtain the emitted power using quantum field theory in curved spacetimes framework at tree level. We compare our results with the scalar synchrotron radiation in Schwarzschild spacetime.
In the companion paper [Phys. Rev. D 103 (2021) 10, [2101.02951]] we have derived the short-ranged potentials for the Teukolsky equations for massless spins $(0,1/2,1,2)$ in general spherically-symmetric and static metrics. Here we apply these results to numerically compute the Hawking radiation spectra of such particles emitted by black holes (BHs) in three different ansatz: charged BHs, higher-dimensional BHs, and polymerized BHs arising from models of quantum gravity. In order to ensure the robustness of our numerical procedure, we show that it agrees with newly derived analytic formulas fo…
The purely thermal nature of Hawking radiation from evaporating black holes leads to the information loss paradox. A possible route to its resolution could be if (enough) correlations are shown to be present in the radiation emitted from evaporating black holes. A re-analysis of Hawking's derivation including the effects of self-interactions in GR shows that the emitted radiation does deviate from pure thermality, however, no correlations exist between successively emitted Hawking quanta. We extend the calculations to Einstein-Gauss-Bonnet gravity and investigate if higher curvature correction…
In this work, we discuss observable characteristics of the radiation emitted from a surface of a collapsing object. We study a simplified model in which a radiation of massless particles has a sharp in time profile and it happens at the surface at the same moment of comoving time. Since the radiating surface has finite size the observed radiation will occur during some finite time. Its redshift and bending angle are affected by the strong gravitational field. We obtain a simple expression for the observed flux of the radiation as a function of time. To find an explicit expression for the flux …
We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate $Γ\sim \exp{(ΔS)}$ arises as a consequence of the first law of thermodynamics, TdS=dE + PdV. Therefore, this approach demonstrates how tunneling is intimately connected with the first law of thermodynamics through the principle of conservation of energy. The analysis is also generally applicable to any reasonable theory of gravity so long as the first law of thermodynamics for horizons holds in the form, TdS=dE + PdV.
Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.
We study the scalar radiation emitted by a source orbiting a Schwarzschild--anti--de Sitter black hole in circular geodesics. We obtain the emitted power using quantum field theory in curved spacetimes at tree level with reflective boundary conditions at infinity. We compare our results with the ones obtained in Schwarzschild and Schwarzschild--de Sitter ($Λ> 0$) spacetimes. In the Schwarzschild-de Sitter spacetime we observe an enhancement of the emitted power associated to the lower multipole modes, when compared with the Schwarzschild case. In contrast, for the Schwarzschild-anti-de Sitter …
General relativistic spherically symmetric matter field with a vanishing stress energy scalar is analyzed. Procedure for generating exact solutions of the field equations for such matter distributions is given. It is further pointed out that all such type I spherically symmetric fields with distinct eignvalues in the radial two space can be treated as a mixture of isotropic and directed radiations. Various classes of exact solutions are given. Junction conditions for such a matter field to the possible exterior solutions are also discussed.
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity …
In a preceding paper [T. Hirayama, Prog. Theor. Phys. 106 (2001), 71], the power of the classical radiation emitted by a moving charge was evaluated in the Rindler frame. In this paper, we give a simpler derivation of this radiation formula, including an estimation of the directional dependence of the radiation. We find that the splitting of the energy-momentum tensor into a bound part I' and an emitted part II' is consistent with the three conditions introduced in the preceding paper, also for each direction within the future light cone.
We study the Hawking radiation emitted into the bulk by $(D+1)$-dimensional Schwarzschild black holes. It is well-known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the `greybody' factors. For intermediate values of $D$ ($3\leq D\lesssim10$), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for $D\gg1$, the typical wavelengths in the black-hole spectrum are much {\it shorter} than the size of the black hole. In this regime, the greybody factors are well described by …
We analyze the scalar radiation emitted from a source rotating around a Schwarzschild black hole using the framework of quantum field theory at the tree level. We show that for relativistic circular orbits the emitted power is about 20% to 30% smaller than what would be obtained in Minkowski spacetime. We also show that most of the emitted energy escapes to infinity. Our formalism can readily be adapted to investigate similar processes.
We investigate numerically the process of the passage of a radiation pulse through a wormhole and the subsequent evolution of the wormhole that is caused by the gravitational action of this pulse. The initial static wormhole is modeled by the spherically symmetrical Armendariz-Picon solution with zero mass. The radiation pulses are modeled by spherically symmetrical shells of self-gravitating massless scalar fields. We demonstrate that the compact signal propagates through the wormhole and investigate the dynamics of the fields in this process for both cases: collapse of the wormhole into the …
Some dynamical aspects of gravitational collapse are explored in this paper. A time-dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with a perfect fluid consisting of two purely radial fluxes -the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of unintercting collapsing shells. Our results show an…
By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.
By studying the Hawking radiation of the most general static spherically symmetric black hole arising from scalar and Dirac particles tunnelling, we find the Hawking temperature is invariant in the general coordinate representation (\ref{arbitrary1}), which satisfies two conditions: a) its radial coordinate transformation is regular at the event horizon; and b) there is a time-like Killing vector.
In this article we study the influence of magnetic fields on the axial gravitational waves emitted during the collapse of a homogeneous dust sphere. We found that while the energy emitted depends weakly on the initial matter perturbations it has strong dependence on the strength and the distribution of the magnetic field perturbations. The gravitational wave output of such a collapse can be up to an order of magnitude larger or smaller calling for detailed numerical 3D studies of collapsing magnetized configurations.
The interplay between acceleration and radiation harbors remarkable and surprising consequences. One of the most striking is that the Larmor radiation emitted by a charge can be seen as a consequence of the Unruh thermal bath. Indeed, this connection between the Unruh effect and classical bremsstrahlung was used recently to propose an experiment to confirm (as directly as possible) the existence of the Unruh thermal bath. This situation may sound puzzling in two ways: first, because the Unruh effect is a strictly quantum effect while Larmor radiation is a classical one, and second, because of …
Motion of massive test particles in the nonvacuum spherically symmetric radiating Vaidya spacetime is investigated, allowing for physical interaction of the particles with the radiation field in terms of which the source energy-momentum tensor is interpreted. This "Poynting-Robertson-like effect" is modeled by the usual effective term describing a Thomson-type radiation drag force. The equations of motion are studied for simple types of motion including free motion (without interaction), purely radial and purely azimuthal (circular) motion, and for the particular case of "static" equilibrium; …
In curved space-time, Hamilton-Jacobi equation is a semi-classical particle's motion equation, which plays an important role in the research of black hole physics. In this paper, starting from Dirac equation describing the spin 1/2 fermion and Rarita-Schwinger equation describing the spin 3/2 fermion respectively, we derive a Hamilton-Jacobi equation of the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling behavior of a charged spherically symmetric black hole is investigated by using this Hamilton-Jacobi equation. The result shows that the…
Stars and black holes are sources of gravitational radiation in many phases of their life, and the signals they emit exhibit features that are characteristic of the generating process. Emitted since the beginning of star formation, these signals also contribute to create a stochastic background of gravitational waves. We shall show how the spectral properties of this background can be estimated in terms of the energy spectrum of each single event and of the star formation rate history, which is now deducible from astronomical observations. We shall further discuss the process of scattering of …
Motivated by the recent work of Robinson and Wilczek, we evaluate the gravitational anomaly of a chiral scalar field in a Vaidya spacetime of arbitrary mass function, and thus the outgoing flux from the time-dependent horizon in that spacetime. We show that this flux differs from that of a perfect blackbody at a fixed temperature. When this flux is taken into account, general covariance in that spacetime is restored. We also generalize their results to the most general static, and spherically symmetric spacetime.
The stability of the Cauchy horizon in spherically symmetric self-similar collapse is studied by determining the flux of scalar radiation impinging on the horizon. This flux is found to be finite.
The gravitational radiation emitted by a rotating magnetic dipole is calculated. Formulas for the polarization amplitudes and the radiated power are obtained in closed forms. A comparison is made with other sources of gravitational and electromagnetic radiation, particularly neutron stars with extremely powerful magnetic fields.
In this paper we present a simple but non-simplistic model of gravitational collapse with thermal emission of pre-Hawking radiation. We apply Einstein equations to a time-dependant spherically symmetric metric and an ultrarelativistic stress-energy tensor. In our model, particles either radially approach the center of the star as collapsing matter, or radially flee from it.
In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherically-symmetric and static metrics. We then compute the short-ranged potentials associated with the radial dynamics of spin 1 and spin 1/2 fields, thereby completing the existing literature on spin 0 and 2. These potentials are crucial for the computation of Hawking radiation and quasi-normal modes emitted by black holes. In addition to the Schwarzschild metric, we apply these results and give the explicit formulas for …
The Einstein equations are integrated in the presence of two (incoming and outgoing) streams of null dust, under the assumptions of spherical symmetry and staticity. The solution is also written in double null and radiation coordinates and it is reinterpreted as an anisotropic fluid. Interior matching with a static fluid and exterior matching with the Vaidya solution along null hypersurfaces is discussed. The connection with two-dimensional dilaton gravity is established.
We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their Newtonian counterparts, though only variables at the null boundary of an asymptotically flat spacetime are used for their definition. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. The results are then compared to other approaches. In particular one obtains unexpected similarities as well as some differen…
We obtain the solution corresponding to a static and spherically symmetric black hole with a cloud of strings (Letelier spacetime) immersed in a quintessential fluid. We discuss some aspects of its thermodynamics. We also present a discussion about Hawking radiation of particles, in the background under consideration.
We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.
In this paper we study the Hawking evaporation of masses of variable-charged Reissner-Nordstrom and Kerr-Newman, black holes embedded into the de Sitter universe by considering the charge to be function of radial coordinate of the spherically symmetric metric.
We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painlevé-Gullstrand coordinates. Near criticality, the system exhibits Choptuik scaling with the added features of a mass gap and a new scaling relationship dependant upon the quantum length scale. The quantum corrected collapse exhibits a radiation-like phase which resolves the singularity: the black hole consists of a compact region of space-time bounded by a single, smooth trapping horizon. The "evaporation" is not complete but leaves behind an outward moving remnant.
Sonic point/photon sphere (SP/PS) correspondence is a theoretical phenomenon which appears in fluid dynamics on curved spacetime and its existence has been recently proved in quite wide situations as theorems. The theorems state that a sonic point (SP) of radiation fluid flow must be on an unstable photon sphere (PS) when the fluid flows radially or rotationally on an equatorial plane in spherically symmetric spacetime of arbitrary dimensions. In this paper, we investigate SP/PS correspondence in spherically, planarly and hyperbolically symmetric spacetime. As the corresponding objects of phot…
We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and non-minimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the non-minimally coupling constant, the spacetime dimension, the cosmological constant and the Gauss-Bonnet coefficient in detail. We find that the non-minimal coupling may suppress the Hawking radiation, while the Gauss-Bonnet coupl…
We establish the formalism in the nonsymmetric gravitational theory (NGT) for stellar equilibrium and gravitational collapse. We study the collapse of a pressureless, spherically symmetric dust cloud. By assuming that the interior solution is smoothly matched at the surface of the star to the quasi-static, spherically symmetric vacuum solution, we find that the star does not collapse to a black hole. It is anticipated that the final collapsed object will reach a state of equilibrium, and will emit thermal, gravitational and other forms of radiation, although the radiation may be emitted only i…
Hawking radiation explicitly depends only on the black hole's total mass, charge and angular momentum. It is therefore generally believed that one cannot reconstruct the information about the initial mass distribution of an object that made the black hole. However, instead of looking at radiation from a static black hole, we can study the whole time-dependent process of the gravitational collapse, and pre-Hawking radiation which is excited because of the time-dependent metric. We compare radiation emitted by a single collapsing shell with that emitted by two concentric shells of the equivalent…
We compute the energy spectra of the gravitational signals emitted when a pointlike mass moves on a closed orbit around a non rotating neutron star, inducing a perturbation of its gravitational field and its internal structure. The Einstein equations and the hydrodynamical equations are perturbed and numerically integrated in the frequency domain. The results are compared with the energy spectra computed by the quadrupole formalism which assumes that both masses are pointlike, and accounts only for the radiation emitted because the orbital motion produces a time dependent quadrupole moment. Th…
The scalar radiation emitted by a source in geodesic circular orbit around a regular Bardeen black hole is analyzed. We use the quantum field theory in curved spacetime framework to obtain the emitted power of radiation by computing the one-particle emission amplitude of scalar particles in the curved background. We compare our results to a similar setting in the spacetime of a Reissner-Nordström black hole.
This article presents the calculation of gravitational and electromagnetic radiation emitted from a classical simple harmonic oscillator (SHO). Here we show only the selected formulae and apply them to a toy problem without rigorous derivation. First, we calculate the explicit expressions for the gravitational waves polarizations and then obtain the power radiated away in gravitational waves using Brans-Dicke theory (BD). We also calculate the electromagnetic dipole and quadrupole power emitted by the SHO and compare them with their gravitational counterparts.
