Kalb-Ramond Research Articles

Accretion of Vlasov gas onto a black hole in the Kalb–Ramond field

Abstract We investigate the accretion of Vlasov gas onto a static, spherically symmetric black hole (BH) influenced by the Kalb–Ramond (KR) field, focusing on the effects of Lorentz symmetry breaking (LSB) parameters. We employ the Maxwell–Jüttner distribution to model the gas at infinity and derive key quantities such as the particle current density and mass accretion rate. Our findings reveal that an increase in the LSB parameter results in a decrease in the mass accretion rate. We also present explicit formulations of the accretion rate in the high-temperature limit and find the result is quite different from the result in Bumblebee model.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Tree-level R4 correction from O(d, d): NS-NS five-point terms

The tree-level string effective action reduced from D to D − d dimensions possesses a continuous O(d, d) symmetry, closely related to T-duality. A necessary condition for a higher derivative correction to preserve this symmetry is that certain O(d, d) violating terms which appear in the dimensional reduction have to cancel out. We use this idea to complete the quartic Riemann correction with all terms involving five NS-NS sector fields. The resulting Lagrangian is considerably simpler than expressions that have previously appeared in the literature.

Kalb-Ramond field and gravitational parity violation

Kalb-Ramond field and gravitational parity violation

Stability analysis of the cosmological dynamics of O(D, D)-complete stringy gravity

The massless fields in the universal NS-NS sector of string theory form O(D, D) multiplets of Double Field Theory, which is a theory that provides a T-duality covariant formulation of supergravity, leading to a stringy modification of General Relativity. In this framework, it is possible to write down the extensions of the Einstein field equations and the Friedmann equations in such a way that the coupling of gravitational and matter sectors is dictated by the O(D, D) symmetry universally. In this paper, we obtain the autonomous form of the O(D, D)-complete Friedmann equations, find the critical points and perform their stability analysis. We also include the phase portraits of the system. Cosmologically interesting cases of scalar field, radiation, and matter are separately considered and compared with the Chameleon models in a similar setting. Accelerating phases and the conditions for their existence are also given for such cases.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Energy extraction and Keplerian fundamental frequencies in the Kalb–Ramond gravity

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb–Ramond field with gravity leads to a power-law hairy BH having a parameter s, which encompasses the Reissner-Nordström black hole (s=1). It is obtained the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb–Ramond black hole, which encompasses, as special cases, Kerr (s=0) and Kerr–Newman (s=1) black holes. With rotating Kalb–Ramond black hole metric, we study its horizon structure and motion of the test particles in the near of the equatorial plane and we determine radial motion equations which governing t and ϕ. We also explore thatthe black hole mass increasing when falling many of mass-less particles are relative to the black hole mass. We consider how the Kalb–Ramond parameters depend on increasing its mass. Furthermore, we analyze the Keplerian frequency, as well as the vertical and horizontal oscillations of basic frequencies, using a graph-based approach. The frequency charts are contingent upon the Kalb–Ramond parameters s and Γ. By consulting certain sources, ones can investigate the distinctions between KR gravity and other models.

Electrically charged black holes in gravity with a background Kalb–Ramond field

We derive the exact solutions for electrically charged black holes both in the absence and presence of a cosmological constant in the gravitational theory with Lorentz violation induced by a background Kalb–Ramond (KR) field. The corresponding thermodynamic properties are investigated. It is found that the standard first law of thermodynamics and the Smarr formula remain valid for the charged KR black holes. Nevertheless, the Lorentz-violating effect influences their ranges of local thermodynamic stability and the first- and second-order phase transition points. Furthermore, to examine the impact of Lorentz violation on the motion of test particles in the spacetime, we analyze the shadow and the innermost stable circular orbit (ISCO) of these black holes. Our results reveal that both the shadow and ISCO radii exhibit a high sensitivity to the Lorentz-violating parameter ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, with a decrease observed as ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document} increases.

New features of circular geodesics in Kalb–Ramond gravity: an autonomous dynamical system approach

Kalb–Ramond gravity is expected to show the signatures of the low energy limit of the Lorentz violating extension of the standard model of particle physics. To understand the theory further, we study the circular geodesics belonging to a class of exact solutions [found recently by Lessa, Silva, Maluf, Almeida (LSMA)] by posing them as a Hamiltonian dynamical autonomous system. The analysis on the phase space for relevant values of the Lorentz violating parameters reveals for the first time a wealth of novel information that include prediction of homoclinic orbits, saddle points, separatrices that are not available from the conventional analysis. Their image on the actual physical space is discussed.

Non-relativistic limits of bosonic and heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Electric Penrose, circular orbits and collisions of charged particles near charged black holes in Kalb–Ramond gravity

General relativity (GR) is a well-tested theory of gravity in strong and weak field regimes. Many modifications to this theory were obtained, including different scalar, vector, and tensor fields to the GR with non-minimal coupling to gravity. Kalb–Ramond (KR) gravity is also a modified theory formulated in the presence of a bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BH). In this work, we study the circular motion of charged particles and explore energetic processes around charged BHs in KR theory. First, we investigated the event horizon radius and analyzed horizon-no horizon regions in the BH charge and KR parameter space. Considering the Coulomb interaction, we derive and analyze the effective potential for charged particles around a charged KR BH. We investigate charged particles’ angular momentum and energy corresponding to circular orbits. We also investigate how the KR non-minimal coupling parameter affects the radius of the innermost stable circular orbits, the corresponding energy, and the angular momentum. We also investigated the electric Penrose process and charged-particle collisions near the KR BH. The presence of the nonzero KR parameter results in a decrease in the energy efficiency of the Penrose process. Also obtained is that the KR parameter’s positive (negative) values cause a decrease (increase) in the center of mass energy of colliding particles near the BH horizon.

Shadow and quasinormal modes of rotating charged black holes in Kalb–Ramond gravity and implications from EHT data

The recent observations of the Event Horizon Telescope for the supermassive black holes M87* and Sgr A* can potentially test gravity theories and acquire further knowledge on black holes and gravity parameters. An essential field of research focuses on the shadow and quasinormal modes of black holes. Therefore, we used the Newman–Janis algorithm to get a rotating charged black hole solution in Kalb–Ramond gravity. Then, we looked at the event horizon radius, the static limit, and the ergoregion of spacetime. We derive the null geodesic equations and the effective potential for photon radial motion. We also investigate how the black hole’s Kalb–Ramond, spin, and charge parameters affect the shadow size and distortion. It is obtained that an increase in the Kalb–Ramond parameter causes a decrease in the radius and increases the distortion of the shadow size. We obtain constraints on black hole charge and spin using the data obtained from Event Horizon Telescope observations of M87* and Sgr A* by testing the effects of the Kalb–Ramond gravity parameter. We examine the energy emission rate using Hawking radiation and demonstrate that a rise in the Kalb–Ramond parameter diminishes this rate. Finally, we calculated and analyzed the typical shadow radius, equatorial, and polar quasinormal modes using the geometric–optic connection between quasinormal mode parameters and conserved quantities along geodesics.

Exact moduli spaces for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2, D = 5 freely acting orbifolds

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on T5 with 0, 1 or 2 hypermultiplets.

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a Schrödinger equation. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

Cosmological implications of Kalb-Ramond-like particles

The Kalb-Ramond field is an antisymmetric, rank-two tensor field which most notably appears in the context of string theory, but has largely been unexplored in the context of cosmology. In this work, motivated by the Kalb-Ramond field in string theory, and antisymmetric tensor fields that emerge in effective field theories ranging from particle physics to condensed matter, we study the primordial production of interacting massive Kalb-Ramond-like-particles (KRLPs). KRLPs contain features of both dark photon and axion models, which can be appreciated via their duality properties. While the massless non-interacting KRLP is dual to a pseudoscalar, and the massive non-interacting KRLP is dual to a pseudovector, the interacting massive KRLP can be distinguished from its scalar and vector counterparts. We study early-universe production of KRLPs via the freeze-in mechanism, considering a ‘dark photon-like’ interaction, an ‘axion-like’ interaction, and a ‘Higgs portal’ interaction, as well as production via cosmological gravitational particle production. We find that as a dark matter candidate, KRLPs can be produced by all of the above mechanisms and account for the relic density of dark matter today for a wide range of masses. Finally, we comment on the potential to obtain both warm and cold dark matter subcomponents, and speculate on observational and experimental prospects.

Tensionless strings in a Kalb-Ramond background

We investigate tensionless (or null) bosonic string theory with a Kalb-Ramond background turned on. In analogy with the tensile case, we find that the Kalb-Ramond field has a non-trivial effect on the spectrum only when the theory is compactified on an (S1)⊗d background with d ≥ 2. We discuss the effect of this background field on the tensionless spectrum constructed on three known consistent null string vacua. We elucidate further on the intriguing fate of duality symmetries in these classes of string theories when the background field is turned on.

β symmetry in type II supergravities

A non geometric sector of the duality group emerging in Kaluza-Klein reductions is realized as an effective symmetry in the low energy action of uncompactified type II theories. This is achieved by extending the so called β symmetry of the universal NS-NS sector to the R-R sector of type IIA, IIB and massive type IIA.

UV and IR effects in axion quality control

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent S-type axion dual to a two form Bμν in 4D and a T-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For T-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why T-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For S-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of m/M with m the axion mass and M the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of p-form gauge potentials (for both p = 2 and p = 3) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.

Mixed boundary conditions in AdS2/CFT1 from the coupling with a Kalb-Ramond field

The open string dual to a 1/6 BPS Wilson line in the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 6 super Chern-Simons-matter theory is coupled to a flat Kalb-Ramond field. We show that the resulting boundary term imposes mixed boundary conditions on the fields that describe the fluctuations on the world-sheet. These boundary conditions fix a combination of the derivatives of the fluctuations, parallel and transverse to the boundary. We holographically compute the correlation functions of insertions on the Wilson line in terms of world-sheet Witten diagrams. We observe that their functional dependence is consistent with the conformal symmetry on the line.

Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field

Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field