scholarly journals SOME ASPECTS OF SPHERICAL SYMMETRIC EXTREMAL DYONIC BLACK HOLES IN 4D N = 1 SUPERGRAVITY

2013 ◽  
Vol 28 (18) ◽  
pp. 1350084 ◽  
Author(s):  
BOBBY E. GUNARA ◽  
FREDDY P. ZEN ◽  
FIKI T. AKBAR ◽  
AGUS SUROSO ◽  
ARIANTO
Keyword(s):  
Black Hole ◽  
Scalar Potential ◽  
Local Existence ◽  
Scalar Fields ◽  
Asymptotic Region ◽  
De Sitter ◽  
Complex Scalar ◽  
Symmetric Black Hole ◽  
Scalar Potentials ◽  
Nonzero Scalar

In this paper, we study several aspects of extremal spherical symmetric black hole solutions of four-dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region, the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and nonzero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincide. In addition, we prove the local existence of nontrivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ℂn-models with both linear superpotential and gauge couplings.

scholarly journals CHARGE ORBITS OF SYMMETRIC SPECIAL GEOMETRIES AND ATTRACTORS

2006 ◽  
Vol 21 (25) ◽  
pp. 5043-5097 ◽  
Author(s):  
STEFANO BELLUCCI ◽  
SERGIO FERRARA ◽  
MURAT GÜNAYDIN ◽  
ALESSIO MARRANI
Keyword(s):  
Black Hole ◽  
Critical Points ◽  
Symmetric Spaces ◽  
Central Charge ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Extremal Black Hole ◽  
Kahler Geometry ◽  
Complex Scalar ◽  
Black Hole Background

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to nV vector multiplets, in an asymptotically flat extremal black hole background described by a 2(nV+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein–Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(nV+1)-dimensional representation RV of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing quartic invariant (for rank-3 spaces). Other than the ½-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

2013 ◽  
Vol 28 (31) ◽  
pp. 1350137 ◽  
Author(s):  
GEUSA DE A. MARQUES ◽  
V. B. BEZERRA ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Cosmic String ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Self ◽  
Dependent Mass ◽  
Scalar Potentials ◽  
Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

scholarly journals Energy of test objects on black hole spacetimes: A brief review

2015 ◽  
Vol 24 (14) ◽  
pp. 1550103 ◽  
Author(s):  
Alejandro Corichi
Keyword(s):  
Black Hole ◽  
Asymptotic Region ◽  
Gravitational Potential Energy ◽  
De Sitter ◽  
Conservation Of Energy ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
Test Particles ◽  
Exterior Regions ◽  
Test Objects

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit different notions of energy as defined by different observers. As is well-known, the existence of a timelike isometry allows for the notion of total conserved energy to be well defined. We use this well-known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the [Formula: see text] Schwarzschild–de Sitter (SdS) case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle’s total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.

scholarly journals Dirac equation with complex potentials

2014 ◽  
Vol 29 (40) ◽  
pp. 1450210 ◽  
Author(s):  
C.-L. Ho ◽  
P. Roy
Keyword(s):  
Dirac Equation ◽  
Scalar Potential ◽  
Complex Potentials ◽  
Zero Energy ◽  
Complex Scalar ◽  
Exact Analytical Solutions ◽  
Exactly Solvable ◽  
Lorentz Scalar ◽  
Scalar Potentials ◽  
Energy Dependent

We study (2+1)-dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy-dependent Schrödinger equations.

scholarly journals Phase transition and geometrical thermodynamics of energy-dependent dilatonic BTZ black holes with power-law electrodynamics

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
M Dehghani ◽  
M Badpa
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Power Law ◽  
Scalar Potential ◽  
Standard Form ◽  
Three Dimensional ◽  
Nonlinear Electrodynamics ◽  
De Sitter ◽  
Field Equations ◽  
Energy Dependent

Abstract The coupled scalar, electromagnetic, and gravitational field equations of Einstein–dilaton gravity theory have been solved in a three-dimensional energy-dependent spacetime and in the presence of power-law nonlinear electrodynamics. The scalar potential is written as the linear combination of two exponential functions, and two families of three-dimensional dilatonic black hole solutions have been introduced which indicate the impacts of rainbow functions on the spacetime geometry. Through consideration of curvature scalars, it has been found that the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. It has been illustrated that, with a suitable choice of parameters, the solutions can produce the two-horizon, extreme and naked singularity black holes. By calculating the black hole charge, mass, entropy, temperature, and electric potential, it has been proved that they fulfill the standard form of the first law of black hole thermodynamics. The thermodynamic stability of the black holes has been analyzed by utilizing the canonical and grand canonical ensembles and noting the signature of the black hole heat capacity and Gibbs free energy of the black holes. The points of type-1, type-2, and Hawking–Page phase transitions and the ranges at which the black holes are locally or globally stable have been determined. The geometrical thermodynamics of the black holes has been studied by use of different thermodynamic metrics, and the results of different approaches have been compared.

scholarly journals Greybody factor and power spectra of the Hawking radiation in the 4D Einstein–Gauss–Bonnet de-Sitter gravity

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Cheng-Yong Zhang ◽  
Peng-Cheng Li ◽  
Minyong Guo
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Equations Of Motion ◽  
Full Range ◽  
Power Spectra ◽  
Massless Scalar ◽  
Coupling Constant ◽  
De Sitter ◽  
Symmetric Black Hole ◽  
Very High

AbstractA novel 4D Einstein–Gauss–Bonnet gravity was recently formulated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. Although this theory may run into trouble at the level of action or equations of motion, the spherically symmetric black hole solution, which can be successfully reproduced in those consistent theories of 4D EGB gravity, is still meaningful and worthy of study. In this paper, we investigate Hawking radiation in the spacetime containing such a de Sitter black hole. Both the greybody factor and the power spectra of the Hawking radiation of the massless scalar are studied numerically for the full range of various parameters, including the GB coupling constant $$\alpha $$ α , the cosmological constant $$\Lambda $$ Λ and the coupling constant related to the scalar filed $$\xi $$ ξ . In particular, we find a negative $$\alpha $$ α leads to a larger greybody factor than that of a $$\alpha \ge 0$$ α ≥ 0 . While, for the power spectra of the Hawking radiation the situation is quite the opposite. The reason is that the temperature of the black hole would be very high when $$\alpha <0$$ α < 0 . Actually, we observe that the temperature would be arbitrarily high when $$\alpha $$ α approaches to the lower bound.

scholarly journals Analytical expressions of copositivity for fourth-order symmetric tensors

2020 ◽  
pp. 1-22 ◽  
Author(s):  
Yisheng Song ◽  
Liqun Qi
Keyword(s):  
Lower Bound ◽  
Fourth Order ◽  
Scalar Potential ◽  
Sufficient Conditions ◽  
Scalar Fields ◽  
Positive Definiteness ◽  
Necessary Condition ◽  
Symmetric Tensors ◽  
Scalar Potentials ◽  
Sufficient And Necessary Condition

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are fourth-order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of fourth-order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for fourth-order 2-dimensional symmetric tensors. For fourth-order 3-dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) copositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for fourth-order 2-dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for fourth-order 2-dimensional symmetric tensors. Finally, these results may be applied to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

scholarly journals Unruh-DeWitt detector responses for complex scalar fields in de Sitter spacetime

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Md Sabir Ali ◽  
Sourav Bhattacharya ◽  
Kinjalk Lochan
Keyword(s):  
Scalar Field ◽  
Response Function ◽  
Scalar Fields ◽  
Detector Response ◽  
Massless Scalar Field ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Complex Scalar ◽  
Sitter Spacetime ◽  
Complex Scalar Field

Abstract We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field ϕ, in the (3 + 1)-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to ϕ†ϕ. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter α-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.

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