8,297 research outputs found
Stability of braneworlds with non-minimally coupled multi-scalar fields
Linear stability of braneworld models constructed with multi-scalar fields is
very different from that of single-scalar field models. It is well known that
both the tensor and scalar perturbation equations of the later can always be
written as a supersymmetric Schr\"{o}dinger equation, so it can be shown that
the perturbations are stable at linear level. However, in general it is not
true for multi-scalar field models and especially there is no effective method
to deal with the stability problem of the scalar perturbations for braneworld
models constructed with non-minimally coupled multi-scalar fields. In this
paper we present a method to investigate the stability of such braneworld
models. It is easy to find that the tensor perturbations are stable. For the
stability problem of the scalar perturbations, we present a systematic
covariant approach. The covariant quadratic order action and the corresponding
first-order perturbed equations are derived. By introducing the orthonormal
bases in field space and making the Kaluza-Klein decomposition, we show that
the Kaluza-Klein modes of the scalar perturbations satisfy a set of coupled
Schr\"{o}dinger-like equations, with which the stability of the scalar
perturbations and localization of the scalar zero modes can be analyzed
according to nodal theorem. The result depends on the explicit models. For
superpotential derived barane models, the scalar perturbations are stable, but
there exist normalizable scalar zero modes, which will result in unaccepted
fifth force on the brane. We also use this method to analyze the
braneworld model with an explicit solution and find that the scalar
perturbations are stable and the scalar zero modes can not be localized on the
brane, which ensure that there is no extra long-range force and the Newtonian
potential on the brane can be recovered.Comment: 13 pages, 3 figure
Born-Infeld Black Holes in 4D Einstein-Gauss-Bonnet Gravity
A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by D.
Glavan and C. Lin [Phys. Rev. Lett. 124, 081301 (2020)], which is intended to
bypass the Lovelock's theorem and to yield a non-trivial contribution to the
four-dimensional gravitational dynamics. However, the validity and consistency
of this theory has been called into question recently. We study a static and
spherically symmetric black hole charged by a Born-Infeld electric field in the
novel four-dimensional Einstein-Gauss-Bonnet gravity. It is found that the
black hole solution still suffers the singularity problem, since particles
incident from infinity can reach the singularity. It is also demonstrated that
the Born-Infeld charged black hole may be superior to the Maxwell charged black
hole to be a charged extension of the Schwarzschild-AdS-like black hole in this
new gravitational theory. Some basic thermodynamics of the black hole solution
is also analyzed. Besides, we regain the black hole solution in the regularized
four-dimensional Einstein-Gauss-Bonnet gravity proposed by H. L\"u and Y. Pang
[arXiv:2003.11552].Comment: 13 pages and 18 figures, published versio
Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime
Most no-hair theorems involve the assumption that the scalar field is
independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the
existence of time-dependent scalar hair outside a stationary black hole in
general relativity was ruled out. We generalize this work to modified gravities
and non-minimally coupled scalar field with an additional assumption that the
spacetime is axisymmetric. It is shown that in higher-order gravity such as
metric gravity the time-dependent scalar hair doesn't exist. While in
Palatini gravity and non-minimally coupled case the time-dependent
scalar hair may exist.Comment: 6 pages, no figure
Gauge invariant hydrogen atom Hamiltonian
For quantum mechanics of a charged particle in a classical external
electromagnetic field, there is an apparent puzzle that the matrix element of
the canonical momentum and Hamiltonian operators is gauge dependent. A
resolution to this puzzle is recently provided by us in [2]. Based on the
separation of the electromagnetic potential into pure gauge and gauge invariant
parts, we have proposed a new set of momentum and Hamiltonian operators which
satisfy both the requirement of gauge invariance and the relevant commutation
relations. In this paper we report a check for the case of the hydrogen atom
problem: Starting from the Hamiltonian of the coupled electron, proton and
electromagnetic field, under the infinite proton mass approximation, we derive
the gauge invariant hydrogen atom Hamiltonian and verify explicitly that this
Hamiltonian is different from the Dirac Hamiltonian, which is the time
translation generator of the system. The gauge invariant Hamiltonian is the
energy operator, whose eigenvalue is the energy of the hydrogen atom. It is
generally time-dependent. In this case, one can solve the energy eigenvalue
equation at any specific instant of time. It is shown that the energy
eigenvalues are gauge independent, and by suitably choosing the phase factor of
the time-dependent eigenfunction, one can ensure that the time-dependent
eigenfunction satisfies the Dirac equation.Comment: 7 pages, revtex4, some further discussion on Dirac Hamiltonian and
the gauge invariant Hamiltonian is added, one reference removed; new address
of some of the authors added, final version to appear in Phys. Rev.
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