arXiv subjects

Philippe Landry

Publications and source records attributed to Philippe Landry.

42 records · Page 3Linked to original sources

arXiv2017

Tidal deformation of a slowly rotating material body: Interior metric and Love numbers

The metric outside a compact body deformed by a quadrupolar tidal field is universal up to its Love numbers, constants which encode the tidal response's dependence on the body's internal structure. For a non-rotating body, the deformed external geometry is characterized by the familiar gravitational Love numbers $K_2^{\text{el}}$ and $K_2^{\text{mag}}$. For a slowly rotating body, these must be supplemented by rotational-tidal Love numbers, which measure the response to couplings between the body's spin and the external tidal field. By integrating the interior field equations, I find that the response of a barotropic perfect fluid to spin-coupled tidal perturbations is described by two rotational-tidal Love numbers, which I calculate explicitly for polytropes. Two other rotational-tidal Love numbers identified in prior work are found to have a fixed, universal value for all barotropes. Equipped with the complete interior solution, I calculate the amplitude of the time-varying internal currents induced by the gravitomagnetic part of the tidal field. For a typical neutron star in an equal-mass binary system, the size of the equatorial velocity perturbation is on the order of kilometers per second.

gr-qc↗

arXiv2015

Dynamical response to a stationary tidal field

We demonstrate that a slowly rotating compact body subjected to a stationary tidal field undergoes a dynamical response, in which the fluid variables and the interior metric vary on the time scale of the rotation period. This dynamical response requires the tidal field to have a gravitomagnetic component generated by external mass currents; the response to a gravitoelectric tidal field is stationary. We confirm that in a calculation carried out to first order in the body's rotation, the exterior geometry bears no trace of this internal dynamics; it remains stationary in spite of the time-dependent interior.

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arXiv2015

Tidal deformation of a slowly rotating material body. External metric

We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric-tracefree tidal moments E_{ab} and B_{ab}, and the body is characterized by its mass M, its radius R, and a dimensionless angular-momentum vector χ^a << 1. The perturbation accounts for all couplings between χ^a and the tidal moments. The body's gravitational response to the applied tidal field is measured in part by the familiar gravitational Love numbers K^{el}_2 and K^{mag}_2, but we find that the coupling between the body's rotation and the tidal environment requires the introduction of four new quantities, which we designate as rotational-tidal Love numbers. All these Love numbers are gauge invariant in the usual sense of perturbation theory, and all vanish when the body is a black hole.

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arXiv2015

Gravitomagnetic response of an irrotational body to an applied tidal field

The deformation of a nonrotating body resulting from the application of a tidal field is measured by two sets of Love numbers associated with the gravitoelectric and gravitomagnetic pieces of the tidal field, respectively. The gravitomagnetic Love numbers were previously computed for fluid bodies, under the assumption that the fluid is in a strict hydrostatic equilibrium that requires the complete absence of internal motions. A more realistic configuration, however, is an irrotational state that establishes, in the course of time, internal motions driven by the gravitomagnetic interaction. We recompute the gravitomagnetic Love numbers for this irrotational state, and show that they are dramatically different from those associated with the strict hydrostatic equilibrium: While the Love numbers are positive in the case of strict hydrostatic equilibrium, they are negative in the irrotational state. Our computations are carried out in the context of perturbation theory in full general relativity, and in a post-Newtonian approximation that reproduces the behavior of the Love numbers when the body's compactness is small.

gr-qc↗

arXiv2014

Relativistic theory of surficial Love numbers

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar, and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

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arXiv2012

The McVittie solution with a negative cosmological constant

Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant ($Λ> 0$), the AdS/CFT correspondence tells us that the case $Λ<0$ is still worthy of consideration. In this paper we study the McVittie solution with $Λ<0$. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson - Walker case, we find that $Λ<0$ ensures collapse to a Big Crunch, a feature which completely dominates the global structure.

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