A well known solution of heterotic string theory is the spinning Kerr-Sen black hole (KSBH) characterized by a string parameter $ξ$. Kerr black hole is recovered at $ξ=0$. The purpose of this paper is to investigate the effect of $ξ$ on a new diagnostic of relative time delay (RTD) to see how the latter deviates from that in general relativity. Assuming KSBH as the spinning lens partner in PSR-BH binary systems, which provide the best laboratory for testing the time delay predictions, we study here the RTD up to third PPN order in $\left(1/r\right)$ in the thin-lens approximation. We work out a useful generalization of the RTD formulas applicable to the experimentally viable \textit{finite} distance lens scales, while\ terms higher than the zeroth order are shown to contain the effect of $ξ$. We shall also relate RTD to the observable image magnification factor determined by $β/θ_{E}$, where $β$ is the angular separation between the source and the observer and $θ_{E}$ is the "Einstein angle" determined by an "effective" non-aligned static lens equivalent to the original aligned spinning lens. Numerical estimates for two typical binary lens systems show $μ$sec level delay at the zeroth order consistent with predictions in the literature. However, the string effect at higher orders is too tiny to be measurable even in the far future leading to the conclusion that the stringy and general relativity BHs are yet observationally indistinguishable.
The explicit form for the post-Newtonian gravitational time delay of light signals propagating on the equatorial plane of a Kerr-Newman black hole is derived. Based on the null geodesic in Kerr-Newman spacetime, we adopt the iterative method to calculate the time delay. Our result reduces to the previous formulation for Kerr black hole if we drop off the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordström geometry is different from the previous publication [Phys. Rev. D 69, 023002 (2004)], in which the largest second-order contribution to the time delay i…
We study the time delay between two relativistic images due to strong gravitational lensing of the light rays caused by the Kerr and Kerr-Newman black holes. The trajectories of the light rays are restricted on the equatorial plane. Using the known form of the deflection angle in the strong deflection limit (SDL) allows us to analytically develop the formalism for the travel time of the light from the distant source winding around the black hole several times and reaching the observer. We find that the black hole with higher mass or with spin of the extreme black hole potentially have higher t…
We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Schäfer's formulation which is based on the retarded Liénard-…
Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbitin…
The scrambling time and its delay are calculated using holography in an asymptotically AdS black hole solution of the gauged Einstein-Maxwell-Dilaton-Axion (EMDA) theory, the dyonic Kerr-Sen-AdS$_4$ black hole, perturbed by rotating and charged shock waves along the equator. The leading term of the scrambling time for a black hole with large entropy is logarithmic in the entropy and hence supports the fast scrambling conjecture for this black hole solution, which implies that the system under consideration is chaotic. We also find that the instantaneous minimal Lyapunov index is bounded by $κ=…
The gravitational lensing of relativistic neutral massive particles caused by a Kerr-Newman black hole is investigated systematically in the weak-field limit. Based on the Kerr-Newman metric in Boyer-Lindquist coordinates, we first derive the analytical form of the equatorial gravitational deflection angle of a massive particle in the third post-Minkowskian approximation. The resulting bending angle, which is found to be consistent with the result in the previous work, is adopted to solve the popular Virbhadra-Ellis lens equation. The analytical expressions for the main observable properties o…
The separated radial part of a massive complex scalar wave equation in the Kerr- Sen geometry is shown to satisfy the generalized spheroidal wave equation which is, in fact, a confluent Heun equation up to a multiplier. The Hawking evaporation of scalar particles in the Kerr-Sen black hole background is investigated by the Damour-Ruffini-Sannan method. It is shown that quantum thermal effect of the Kerr-Sen black hole has the same character as that of the Kerr-Newman black hole.
The separated radial part of a massive complex scalar wave equation in the Kerr-Sen geometry is shown to satisfy the generalized spheroidal wave equation which is, in fact, a confluent Heun equation up to a multiplier. The Hawking evaporation of scalar particles in the Kerr-Sen black hole background is investigated by the Damour-Ruffini-Sannan's method. It is shown that quantum thermal effect of the Kerr-Sen black hole has the same characteras that of the Kerr-Newman black hole.
We study the collision of two uncharged spinning particles around an extreme Kerr-Sen black hole and calculate the maximal efficiency of the energy extraction from the Kerr-Sen black hole via super Penrose process. We consider the collision of two massive particles as well as collision of a massless particle with a massive particle. For all the cases, we find that the maximum efficiency decreases as the Kerr-Sen black hole's parameter($b=1-a$) increases.
In this work we investigate validity of the weak form of the cosmic censorship conjecture in the interaction of Kerr-Sen black holes with neutral test fields. Previous studies of the Klein-Gordon equation on Kerr-Sen background imply that superradiance occurs for scalar fields. We show that scalar fields can overspin a nearly extremal black hole into a naked singularity, but the modes that could overspin an extremal black hole are not absorbed due to superradiance. From Kerr analogy one can naively expect superradiance to be absent for fermionic fields. In such a case overspinning becomes gene…
In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies $ω$ and angular quantum numbers $λ$, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate as well as efficient method for investigating…
The correspondence between the shadow radius and the quasi-normal modes of the Kerr-Sen black hole is studied. By using the equation of the shadow radius of the Kerr-Sen black hole and the angular separation constant of the quasi-normal modes, the expression of the real part of quasi-normal modes related to the shadow radius is obtained. We found that in the eikonal limit, our formula coincides with the previous result. Moreover, we also calculate the energy emission rate of the Kerr-Sen black hole, it turns out that the peak energy emissivity is inversely correlated with the charge parameter.
Here we consider static, axially symmetric, rotating and charged Kerr-Sen Dilaton-Axion black hole metric in generalized Boyer-Lindquist coordinates as particle accelerators. We obtain the geodesic motions of particle. We find the effective potential and discuss the circular orbit of a particle. We investigate the center of mass energy of two colliding neutral particles with different rest masses falling from rest at infinity to near the non-extremal horizons (event horizon and Cauchy horizon) and extremal horizon of the Kerr-Sen black hole. Analogous to the Compton process, we discuss the col…
We investigate the charged scalar pair production near the horizon of a near-extremal Kerr-Sen black holes. The condition for pair production to occur has relation to the violation of Breitenlohner-Freedman bound in an AdS$_2$ space. The method employed in this work has been used to show the pair production in the near-horizon of a near-extremal Kerr-Newman black hole and its non-rotating case as well. We also discuss the static limit of our result.
By neglecting the self-force, self-energy, and radiative effects, it has been shown that an extremal or near-extremal Kerr-Newman black hole can turn into a naked singularity when it captures charged and spinning massive particles. A straightforward question then arises: do charged and rotating black holes in string theory possess the same property? In this paper we apply the Wald's gedanken experiment, in his study on the possibility of destroying extremal Kerr-Newman black holes, to the case of (near-)extremal Kerr-Sen black holes. We find that feeding a test particle into a (near-)extremal …
We investigate periodic orbits and zoom-whirl behaviors around a Kerr Sen black hole with a rational number $q$ in terms of three integers $(z,w,v)$, from which one can immediately read off the number of leaves(or zooms), the ordering of the leaves, and the number of whirls. The characteristic of zoom-whirl periodic orbits is the precession of multi-leaf orbits in the strong field regime. This feature is analogous to the counterpart in the Kerr space-time. Finally, we analyze the impact of the charge parameter $b$ on the zoom-whirl periodic orbits. Compared to the periodic orbits around the Ke…
In this article we study the innermost stable circular orbit (ISCO) of electrically charged particles in the electrically charged Reissner-Nordström spacetime, the Kerr-Newman spacetime and the Kerr-Sen spacetime. We find that the radius of the ISCO increases with an increasing particle-black hole charge product $|qQ|$ in the case of attractive Coulomb interaction $qQ<0$. For repulsive Coulomb interaction, the ISCO radius first decreases to a minimum and then increases again, until it diverges as the charge product approaches one. If the charge $Q$ of the black hole is very small, the minimum …
In this study, we consider charged massive scalar fields around a Kerr-Sen spacetime. The radial and angular parts of the covariant Klein-Gordon equation are solved in terms of the confluent Heun function. From the exact radial solution, we obtain the Hawking radiation spectrum and discuss its resonant frequencies. The massless case of the resonant frequencies is also examined.
We present firstly equation of motion for the photon coupled to Weyl tensor in a Kerr black hole spacetime and then study further the corresponding strong gravitational lensing. We find that black hole rotation makes propagation of the coupled photons more complicated, which brings some new features for physical quantities including the marginally circular photon orbit, the deflection angle, the observational gravitational lensing variables and the time delay between two relativistic images. There is a critical value of the coupling parameter for existence of the marginally circular photon orb…
In this paper, we show the additive separation of the Hamilton-Jacobi equation, present the 4-velocity of the test particles, and attempt to find the equatorial circular photon orbit (ECPO) in the Kerr-Sen-Taub-NUT (KSTN) solution of the low energy limit of heterotic string theory. In the process of trying to find the ECPO, we instead encounter a ring singularity that could be outside the horizon of the KSTN black hole.
We present a novel solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed. We also study the test body circular equatorial motions in the spacetime.
We analytically study the optical appearance of an isotropically emitter orbiting near the horizon of a near-extremely rotating Kerr-Sen (KS) black hole which is an electrically charged black hole arising in heterotic string theory. We study the influence of the Sen charge on the observational quantities, including the image position, flux and redshift factor. Moreover, we compare the results with those for a near-extremal Kerr-Newman (KN) black hole, which is the charged rotating black hole in general relativity. We find quantitative corrections of the signatures of these charged black holes …
The advent of gravitational wave observation starts a new era of precision tests of gravitational theory. Estimations of black holes mergers should come from any well established gravitational theories, provided that the theory has not been ruled out by observations. In this paper we consider the low energy limit of heterotic string theory where the associated rotating and charged black holes are described by the Kerr-Sen solution. We investigate the approximate final spins and quasinormal modes of the black hole resulting from the merger process.
It is reported that Kerr-Newman and Kerr-Sen black holes are unstable to perturbations of charged massive scalar field. In this paper, we study analytically the complex frequencies which characterize charged massive scalar fields in a near-extremal Kerr-Sen black hole. For near-extremal Kerr-Sen black holes and for charged massive scalar fields in the eikonal large-mass $\mathcal{M}\gg μ$ regime, where $\mathcal{M}$ is the mass of the black hole, and $μ$ is the mass of the charged scalar field, we have obtained a simple expression for the dimensionless ratio $ω_I /\left(ω_R - ω_c\right)$, wher…
We study thermodynamics of the four-dimensional Kerr-Sen-AdS black hole and its ultra-spinning counterpart, and verify that both black holes fullfil the first law and Bekenstein-Smarr mass formulae of black hole thermodynamics. Furthermore, we derive new Christodoulou-Ruffini-like squared-mass formulae for the usual and ultra-spinning Kerr-Sen-AdS$_4$ solutions. We show that this ultra-spinning Kerr-Sen-AdS$_4$ black hole does not always violate the Reverse Isoperimetric Inequality (RII) since the value of the isoperimetric ratio can be larger/smaller than, or equal to unity, depending upon wh…
The recent time witnessed a surge of interest in strong gravitational lensing by black holes is due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in both general relativity and heterotic string theory. That may help us to assess the phenomenological differences between these models. Motivated by this, we consider gravitational lensing by the nonsingular Kerr-Sen black holes, which encompass Kerr black holes as a particular case, to calculate the light deflection coefficients $p$ and $q$ in strong-field limits, while the former increases with incre…
We study the gravitational lensing by a Kerr-Sen Black Hole arising in heterotic string theory. A closed form expression for the bending angle of light in equatorial plane of Kerr-Sen Black Hole is derived as a function of impact parameter, spin and charge of the Black Hole. Results obtained are also compared with the corresponding cases of Kerr Black Hole in general relativity. It is observed that charge parameter behaves qualitatively similar as the spin parameter for photons travelling in direct orbits while behaves differently for photons in retrograde orbits around Black Hole. As the nume…
We consider the time delay of interfering single photons oppositely traveling in the Kerr metric of a rotating massive object. Classically, the time delay shows up as a phase difference between coherent sources of light. In quantum mechanics, the loss in visibility due to the indistinguishability of interfering photons is directly related to the time delay. We can thus observe the Kerr frame-dragging effect using the Hong-Ou-Mandel (HOM) dip, a purely quantum mechanical effect. By Einstein's equivalence principle, we can analogously consider a rotating turntable to simulate the Kerr metric. We…
Deflection of Light due to Kerr Sen Black Hole in Heterotic String Theory using Material Medium Approach
National Institute of Technology, Agartala（阿加塔拉国家理工学院）；The Institute of Mathematical Sciences（数学科学研究所）；Hemvati Nandan Bahuguna Garhwal Central University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔中央大学）；Center for Space Research, North-West University（西北大学空间研究中心）；Assam University（阿萨姆大学）
We investigate the geodesic motion in the background of Kerr-Sen Black Hole arising in the heterotic string theory. The nature of effective potential is discussed in radial as well as latitudinal direction. A special class of spherical photon orbits is obtained along with the expression for the turning point for radial photons. Dependence of photon motion within this class of solution is discussed explicitly in view of the different Black Hole parameters. We have discussed the allowed regions for geodesic motion of massless test particles around Kerr- Sen Black Hole in more generalised way by …
It has been proved that arbitrarily high-energy collision between two particles can occur near the horizon of an extremal Kerr black hole as long as the energy $E$ and angular momentum $L$ of one particle satisfies a critical relation, which is called the BSW mechanism. Previous researchers mainly concentrate on geodesic motion of particles. In this paper, we will take spinning particle which won't move along a timelike geodesic into our consideration, hence, another parameter $s$ describing the particle's spin angular momentum was introduced. By employing the Mathisson-Papapetrou-Dixon equati…
We present a new choice of initial data for binary black hole simulations that significantly improves the efficiency of high-spin simulations. We use spherical Kerr-Schild coordinates, where the horizon of a rotating black hole is spherical, for each black hole. The superposed spherical Kerr-Schild initial data reduce the runtime by a factor of 2 compared to standard superposed Kerr-Schild for an intermediate resolution spin-0.99 binary-black-hole simulation. We also explore the possibility of delaying the transition from the initial data gauge to the evolution gauge, which produces an additio…
Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colours. It is expected, however, that at certain scales new physics, in particular in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, whic…
The \textit{exact} Sagnac delay in the Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin $a\rightarrow 0$, the delay does not vanish. This fact is similar to the non-vanishing of Lense-Thirring precession under $a\rightarrow 0$ even though t…
We analyze the shadow of charged stationary axially symmetric space-time (Kerr-Sen dilaton-axion black hole). This black hole is defined by a mass $M$, a spin $a$ and $r_α=Q^{2}/M$, where $Q$ is the electric charge. Shadows are investigated in two conditions, i) for an observer at infinity in vacuum and ii) for an observer at infinity in the presence of plasma with radial power-low density. In vacuum, the shadow of this black hole depends on charge and spin parameter. We can see that, increasing electric charge, $Q$ decreases the size of shadow. Also, increasing spin parameter $a$ decreases th…
Assuming that a particle source is at rest in a locally non-rotating frame on the equatorial plane of the Kerr-Sen black hole, we investigate the escape of the massless particle and massive particle from the black hole to spatial infinity. We calculate the escape probabilities of the emitted particles. We find that the angular momentum of the Kerr-Sen black hole boosts the escape probabilities near the horizon of the extreme Kerr-Sen black hole; however the angular momentum of the Kerr-Sen black hole suppresses the escape probabilities near the horizon of the non-extreme Kerr-Sen black hole. W…
Gravitational lensing around a Kerr-Sen black hole in plasma background
National Institute of Technology, Agartala（阿加塔拉国家理工学院）；The Institute of Mathematical Sciences（数学科学研究所）；Hemvati Nandan Bahuguna Garhwal Central University（赫马瓦蒂·南丹·巴胡加纳加尔瓦尔中央大学）；Centre for Space Research, North-West University（西北大学空间研究中心）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）
Quantum gravitational effects on the near horizon may alter the black hole's horizon drastically to be partially reflective, portrayed by a quantum membrane. With this modification, the object can be considered as an exotic compact object (ECO). Quantum effects on the strong gravitational regime may also lead to a non-conserved matter tensor that can be described phenomenologically using Rastall gravity. In this work, we study the properties of black holes and ECOs within Rastall gravity using Kerr/CFT correspondence. We systematically investigate the properties of the most general rotating bl…
We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extensi…
Topological signatures in Kerr-Sen AdS black hole thermodynamics
Centre for Theoretical Physics, Jamia Millia Islamia（贾米亚米利亚伊斯兰大学理论物理中心）；Department of Physics, Mahishadal Raj College（马希沙达尔皇家学院物理系）；Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University（兰州大学理论物理研究所与引力研究中心）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal（夸祖鲁-纳塔尔大学数学、统计与计算机科学学院天体物理学与宇宙学研究中心）
We give an explicit expression for the frequencies of slowly damped quasinormal modes of near-extreme Kerr black holes. It follows from this expression that the near-extreme Kerr holes obey the Hod's bound: in the limit of maximal rotation, $\lim \sup ω_{IS}/T\leq π/ \hbar$, where $ω_{IS}$ is the decay rate of the slowest decaying quasinormal mode, $T$ is the black hole temperature. On the other hand, the bound is not saturated in the sense that $\lim \inf ω_{IS}/T< π/\hbar$ is a strict inequality. {\it It remains unclear} whether the bound is saturated in the sense that $\lim \sup ω_{IS}/T= π…
The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black ho…
Behaviour of singularities of the rotating black holes under an arbitrary boost is considered on the basis of a complex representation of the Kerr theorem. We give a simple algorithm allowing to get explicit expressions for the metric and the position of the singularities for arbitrary direction and magnitude of the boost, including the ultrarelativistic case. The non-smoothness of the ultrarelativistic limit is discussed. The Kerr-Sen BH-solution to low energy string theory is also analyzed.
