I unfortunately cannot remember the title or author of this book, but can summarize various plot points and details.
The principle motion technology is named "counter mass", a form of localized space warp used on everything from fighter jets, space torpedoes to larger ships.
One of the Earth nations (there are several) develops tachyon technology. This "tachyon drive" allows them to make journeys nearly anywhere instantly, compared to the days required for counter-mass transit between stars.
If I recall correctly, the ship is named the "Odyssey". I remember this because the replacement ship they build at the end of the book is powered by two black holes and is named the "Odysseus".
They teleport to another location in the galaxy and encounter a race of highly advanced humans that are nonetheless surprised at these strange abilities of the earthlings. The advanced race has extremely powerful shields, lasers and transit abilities using some kind alternate dimension. It still takes them a few weeks to cross the galaxy.
A race of liquid metal beings is awakened by the human activity. They invade Earth.
The Odyssey also features "t cannons" or tachyon cannons which teleport atomic bombs directly inside the ships of their enemies.
The Odyssey changes colors to reduce damage from enemy lasers.
The Odyssey is almost completely undetectable to enemy ships whose sensors are used to track captured suns and black holes. The Odyssey, meanwhile, uses mere fission and is thus overlooked.
At the end of the book, the metal aliens invade Earth but are repelled. The earthlings form an alliance with the advanced humans. The Odysseus is built. One character thinks to herself that the black hole seemed sapient, somehow.