State the value of the Ricci tensor R on the event horizon of a Schwarzschild black hole, and justify your answer.
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Q: Question A5 State the value of the Ricci tensor R on the event horizon of a Schwarzschild black…
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- Please don't prvide handwritten solution...The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is 1014 GeV/c2 .(a) How many proton masses is this?(b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity γ would have to be.)Consider some inertial observers S, S' and S" in the standard configuration and such that observer S' has velocity v₁ with respect to S, whilst S" has velocity v₂ with respect to S'. Then, according to the Newtonian Framework (i.e., using Galilean transformations), the velocity of S" with respect to S is: Select one: O a. -V₁ + V₂ O b. V₁ + 2 V₂ OC. V₁ V₂ O d. V₁ + V₂
- Two beams of light are shot simultaneously from the middle of a train towards its front and rear, respectively. The train is moving in a straight line with constant velocity v < c with respect to a certain train station. For an observer moving with the train, and according to the theory of Special Relativity, which light ray reaches its destination first? Will someone standing at the station agree with this observation? Select one: O a. The light ray that moves in the same direction as the train will arrive first. Someone at the train station will agree. O b. The light rays will arrive simultaneously. Someone at the train station will not agree. O c. The light ray that moves in the same direction as the train will arrive first. Someone at the train station will not agree. Od. The light rays will arrive simultaneously. Someone at the train station will agree.Show that if two particles with mass collide and fuse together, the mass of the fused system will always be larger than the collective masses of the individual components. Along with your proof, account for the increase in mass. (assume the particles are travelling with equal but opposite velocities within a particular reference frame.) Show that a normal vector to the horizon three-surface of a Schwarzschild black hole is a null vector.Please answer D A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) An observer standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-based observer also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignore the relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligibly small compared to 0.800c. a) According to a scientist in the spaceship, the Earth-Sun distance is: 8.976 x 1010m b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is: 357s c) What is the ratio of the kinetic energy to rest energy of the spaceship? KE/ER = 0.667 d) As the spaceship passed over the Sun, the alien scientist launched a probe toward Earth, traveling at 0.200c relative to the spaceship. What would the…
- Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is, only take into account three axes, two axes that define the xy plane characterized by the spatial coordinates x and y, and a third axis perpendicular to the xy plane that corresponds to the temporal coordinate t (ct so that the three axes have the same dimensions ). This coordinate system S is in which an observer O describes the events that occur in the Universe from his point of view a) Draw the world line of a particle moving in the xy plane describing a circle with constant speed. b) Draw the world line of a particle that is accelerating from rest until it reaches a certain speed, which already remains constant. c) Now drop the spatial coordinate y. On the plane (x, ct) that describes the events seen by the observer O in his system S and considering the Lorentz transformations, draw the axes for a system S' in which an observer O' would describe the events that occur in the universe.…A beam of π+meson (pions) at Fermilab are traveling at a speed of 0.92cwithrespect to the laboratory. The proper mean lifetime for these pions is 2.6×10−8s.(a) Is this proper lifetime measured in the laboratory frame or the frame of the pions?Why? (b) What is the mean lifetime as measured in the other frame of reference?The Tevatron was a large particle accelerator that would collide beams ofprotons and anti-protons to see what would come out of the collisions.a) Let’s assume that each particle (in both beams) was accelerated to a total energy of100 GeV. What is the speed of the protons (relative to the speed of light) if you assumethe mass of the proton is equal to 1 GeV/c^2? Write your answer in terms of the speed oflight—keep it as a decimal times “c”. You will need several decimal places.b) Suppose that you now accelerate each particle to a speed of 0.9c. Since they are movingin opposite directions, what is the speed that one would measure for the speed of the otherparticle? Just give the absolute value of this speed. Don’t worry about the sign.c) Given your answer in part b, what is the energy of that one particle would measure forthe other particle?
- An accretion disc may form around a black hole. This is a thin disc of orbiting matter spanning radii r = Rin to Rout around the black hole. We assume that Rout » Rin and so we make the simplifying approximation that Rout → +∞o. The disc radiates according to the following equation 3 GM D(r, 0) = 1 CM (1-[B]"). 4 3 Here, r and are the usual polar coordinates with the origin at the centre of the disc. G is the gravitational constant, M is the mass of the black hole, Rin is the disc inner radius, M is the accretion rate - all these are constants. (a) Integrate D(r, 0) over the surface of the disc to find the total radiation output of the disc. (b) Find the total radiation in the case of Rin = 6GM/c².A new theory predicts that a chargino x¯ of mass m(x¯¯) = 620 GeV decays into a neutralino x with a mass of m(x) = 171 GeV and a W boson with a mass of m(W) 80.4 GeV. a) Calculate the energy of the neutralino in the rest frame of the chargino.Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is, only take into account three axes, two axes that define the xy plane characterized by the spatial coordinates x and y, and a third axis perpendicular to the xy plane that corresponds to the temporal coordinate t (ct so that the three axes have the same dimensions ). This coordinate system S is in which an observer O describes the events that occur in the Universe from his point of viewc) Now drop the spatial coordinate y. On the plane (x, ct) that describes the events seen by the observer O in his system S and considering the Lorentz transformations, draw the axes for a system S' in which an observer O' would describe the events that occur in the universe. We must create a space-time diagram for the scenario presented in the problem. Only the x, y, and ct-axis must be taken into consideration. Thus, we have our three dimensions (ct, x, y). We'll remain with relativistic units for the…